Matemática discreta Ejemplos

⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 3 & 1 & - 3 1 & - 2 & - 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 1 & 1 \\ 3 & 1 & - 3 \\ 1 & - 2 & - 5 \end{array}]$

Paso 1

Escribe la matriz como un producto de una matriz triangular inferior y una matriz triangular superior.

⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 l_{21} & 1 & 0 l_{31} & l_{32} & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} u_{11} & u_{12} & u_{13} 0 & u_{22} & u_{23} 0 & 0 & u_{33} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 3 & 1 & - 3 1 & - 2 & - 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 0 & 0 \\ l_{21} & 1 & 0 \\ l_{31} & l_{32} & 1 \end{array}] [\begin{array}{c} u_{11} & u_{12} & u_{13} \\ 0 & u_{22} & u_{23} \\ 0 & 0 & u_{33} \end{array}] = [\begin{array}{c} 1 & 1 & 1 \\ 3 & 1 & - 3 \\ 1 & - 2 & - 5 \end{array}]$

Paso 2

Multiplica

⎡ ⎢ ⎣ \begin{matrix} 1 & 0 & 0 l_{21} & 1 & 0 l_{31} & l_{32} & 1 \end{matrix} ⎤ ⎥ ⎦ ⎡ ⎢ ⎣ \begin{matrix} u_{11} & u_{12} & u_{13} 0 & u_{22} & u_{23} 0 & 0 & u_{33} \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 & 0 & 0 \\ l_{21} & 1 & 0 \\ l_{31} & l_{32} & 1 \end{array}] [\begin{array}{c} u_{11} & u_{12} & u_{13} \\ 0 & u_{22} & u_{23} \\ 0 & 0 & u_{33} \end{array}]$ .

Toca para ver más pasos...

Paso 2.1

Dos matrices pueden multiplicarse solo si el número de columnas en la primera matriz es igual al número de filas en la segunda matriz. En este caso, la primera matriz es

3 \times 3

$3 \times 3$ y la segunda matriz es

3 \times 3

$3 \times 3$ .

Paso 2.2

Multiplica cada fila en la primera matriz por cada columna en la segunda matriz.

⎡ ⎢ ⎣ \begin{matrix} 1 u_{11} + 0 \cdot 0 + 0 \cdot 0 & 1 u_{12} + 0 u_{22} + 0 \cdot 0 & 1 u_{13} + 0 u_{23} + 0 u_{33} l_{21} u_{11} + 1 \cdot 0 + 0 \cdot 0 & l_{21} u_{12} + 1 u_{22} + 0 \cdot 0 & l_{21} u_{13} + 1 u_{23} + 0 u_{33} l_{31} u_{11} + l_{32} \cdot 0 + 1 \cdot 0 & l_{31} u_{12} + l_{32} u_{22} + 1 \cdot 0 & l_{31} u_{13} + l_{32} u_{23} + 1 u_{33} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 3 & 1 & - 3 1 & - 2 & - 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} 1 u_{11} + 0 \cdot 0 + 0 \cdot 0 & 1 u_{12} + 0 u_{22} + 0 \cdot 0 & 1 u_{13} + 0 u_{23} + 0 u_{33} \\ l_{21} u_{11} + 1 \cdot 0 + 0 \cdot 0 & l_{21} u_{12} + 1 u_{22} + 0 \cdot 0 & l_{21} u_{13} + 1 u_{23} + 0 u_{33} \\ l_{31} u_{11} + l_{32} \cdot 0 + 1 \cdot 0 & l_{31} u_{12} + l_{32} u_{22} + 1 \cdot 0 & l_{31} u_{13} + l_{32} u_{23} + 1 u_{33} \end{array}] = [\begin{array}{c} 1 & 1 & 1 \\ 3 & 1 & - 3 \\ 1 & - 2 & - 5 \end{array}]$

Paso 2.3

Simplifica cada elemento de la matriz mediante la multiplicación de todas las expresiones.

⎡ ⎢ ⎣ \begin{matrix} u_{11} & u_{12} & u_{13} l_{21} u_{11} & l_{21} u_{12} + u_{22} & l_{21} u_{13} + u_{23} l_{31} u_{11} & l_{31} u_{12} + l_{32} u_{22} & l_{31} u_{13} + l_{32} u_{23} + u_{33} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 3 & 1 & - 3 1 & - 2 & - 5 \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} u_{11} & u_{12} & u_{13} \\ l_{21} u_{11} & l_{21} u_{12} + u_{22} & l_{21} u_{13} + u_{23} \\ l_{31} u_{11} & l_{31} u_{12} + l_{32} u_{22} & l_{31} u_{13} + l_{32} u_{23} + u_{33} \end{array}] = [\begin{array}{c} 1 & 1 & 1 \\ 3 & 1 & - 3 \\ 1 & - 2 & - 5 \end{array}]$

⎡ ⎢ ⎣ \begin{matrix} u_{11} & u_{12} & u_{13} l_{21} u_{11} & l_{21} u_{12} + u_{22} & l_{21} u_{13} + u_{23} l_{31} u_{11} & l_{31} u_{12} + l_{32} u_{22} & l_{31} u_{13} + l_{32} u_{23} + u_{33} \end{matrix} ⎤ ⎥ ⎦ = ⎡ ⎢ ⎣ \begin{matrix} 1 & 1 & 1 3 & 1 & - 3 1 & - 2 & - 5 \end{matrix} ⎤ ⎥ ⎦

Paso 3

Resuelve.

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Paso 3.1

Escribe como un sistema de ecuaciones lineales

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{11} = 3

$l_{21} u_{11} = 3$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{11} = 1

$l_{31} u_{11} = 1$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2

Resuelve el sistema de ecuaciones.

Toca para ver más pasos...

Paso 3.2.1

Reemplaza todos los casos de

u_{11}

$u_{11}$ por

1

$1$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.1.1

Reemplaza todos los casos de

u_{11}

$u_{11}$ en

l_{21} u_{11} = 3

$l_{21} u_{11} = 3$ por

1

$1$ .

l_{21} \cdot 1 = 3

$l_{21} \cdot 1 = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{11} = 1

$l_{31} u_{11} = 1$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2.1.2

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.1.2.1

Multiplica

l_{21}

$l_{21}$ por

1

$1$ .

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{11} = 1

$l_{31} u_{11} = 1$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{11} = 1

$l_{31} u_{11} = 1$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2.1.3

Reemplaza todos los casos de

u_{11}

$u_{11}$ en

l_{31} u_{11} = 1

$l_{31} u_{11} = 1$ por

1

$1$ .

l_{31} \cdot 1 = 1

$l_{31} \cdot 1 = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2.1.4

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.1.4.1

Multiplica

l_{31}

$l_{31}$ por

1

$1$ .

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2.2

Reemplaza todos los casos de

l_{31}

$l_{31}$ por

1

$1$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.2.1

Reemplaza todos los casos de

l_{31}

$l_{31}$ en

l_{31} u_{12} + l_{32} u_{22} = - 2

$l_{31} u_{12} + l_{32} u_{22} = - 2$ por

1

$1$ .

1 \cdot u_{12} + l_{32} u_{22} = - 2

$1 \cdot u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2.2.2

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.2.2.1

Multiplica

u_{12}

$u_{12}$ por

1

$1$ .

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$

Paso 3.2.2.3

Reemplaza todos los casos de

l_{31}

$l_{31}$ en

l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5

$l_{31} u_{13} + l_{32} u_{23} + u_{33} = - 5$ por

1

$1$ .

1 \cdot u_{13} + l_{32} u_{23} + u_{33} = - 5

$1 \cdot u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

Paso 3.2.2.4

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.2.4.1

Multiplica

u_{13}

$u_{13}$ por

1

$1$ .

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

Paso 3.2.3

Reemplaza todos los casos de

l_{21}

$l_{21}$ por

3

$3$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.3.1

Reemplaza todos los casos de

l_{21}

$l_{21}$ en

l_{21} u_{12} + u_{22} = 1

$l_{21} u_{12} + u_{22} = 1$ por

3

$3$ .

3 \cdot u_{12} + u_{22} = 1

$3 \cdot u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

Paso 3.2.3.2

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.3.2.1

Multiplica

3

$3$ por

u_{12}

$u_{12}$ .

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$

Paso 3.2.3.3

Reemplaza todos los casos de

l_{21}

$l_{21}$ en

l_{21} u_{13} + u_{23} = - 3

$l_{21} u_{13} + u_{23} = - 3$ por

3

$3$ .

3 \cdot u_{13} + u_{23} = - 3

$3 \cdot u_{13} + u_{23} = - 3$

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.3.4

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.3.4.1

Multiplica

3

$3$ por

u_{13}

$u_{13}$ .

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.4

Reemplaza todos los casos de

u_{12}

$u_{12}$ por

1

$1$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.4.1

Reemplaza todos los casos de

u_{12}

$u_{12}$ en

3 u_{12} + u_{22} = 1

$3 u_{12} + u_{22} = 1$ por

1

$1$ .

3 (1) + u_{22} = 1

$3 (1) + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.4.2

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.4.2.1

Multiplica

3

$3$ por

1

$1$ .

3 + u_{22} = 1

$3 + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

3 + u_{22} = 1

$3 + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.4.3

Reemplaza todos los casos de

u_{12}

$u_{12}$ en

u_{12} + l_{32} u_{22} = - 2

$u_{12} + l_{32} u_{22} = - 2$ por

1

$1$ .

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 + u_{22} = 1

$3 + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.4.4

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.4.4.1

Elimina los paréntesis.

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 + u_{22} = 1

$3 + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 + u_{22} = 1

$3 + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 + u_{22} = 1

$3 + u_{22} = 1$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.5

Reemplaza todos los casos de

u_{13}

$u_{13}$ por

1

$1$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.5.1

Mueve todos los términos que no contengan

u_{22}

$u_{22}$ al lado derecho de la ecuación.

Toca para ver más pasos...

Paso 3.2.5.1.1

Resta

3

$3$ de ambos lados de la ecuación.

u_{22} = 1 - 3

$u_{22} = 1 - 3$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.5.1.2

Resta

3

$3$ de

1

$1$ .

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.5.2

Reemplaza todos los casos de

u_{13}

$u_{13}$ en

3 u_{13} + u_{23} = - 3

$3 u_{13} + u_{23} = - 3$ por

1

$1$ .

3 (1) + u_{23} = - 3

$3 (1) + u_{23} = - 3$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.5.3

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.5.3.1

Multiplica

3

$3$ por

1

$1$ .

3 + u_{23} = - 3

$3 + u_{23} = - 3$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

3 + u_{23} = - 3

$3 + u_{23} = - 3$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.5.4

Reemplaza todos los casos de

u_{13}

$u_{13}$ en

u_{13} + l_{32} u_{23} + u_{33} = - 5

$u_{13} + l_{32} u_{23} + u_{33} = - 5$ por

1

$1$ .

1 + l_{32} u_{23} + u_{33} = - 5

$1 + l_{32} u_{23} + u_{33} = - 5$

3 + u_{23} = - 3

$3 + u_{23} = - 3$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

Paso 3.2.5.5

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.5.5.1

Elimina los paréntesis.

1 + l_{32} u_{23} + u_{33} = - 5

$1 + l_{32} u_{23} + u_{33} = - 5$

3 + u_{23} = - 3

$3 + u_{23} = - 3$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

1 + l_{32} u_{23} + u_{33} = - 5

$1 + l_{32} u_{23} + u_{33} = - 5$

3 + u_{23} = - 3

$3 + u_{23} = - 3$

u_{22} = - 2

$u_{22} = - 2$

1 + l_{32} u_{22} = - 2

$1 + l_{32} u_{22} = - 2$

l_{31} = 1

$l_{31} = 1$

l_{21} = 3

$l_{21} = 3$

u_{11} = 1

$u_{11} = 1$

u_{12} = 1

$u_{12} = 1$

u_{13} = 1

$u_{13} = 1$

1 + l_{32} u_{23} + u_{33} = - 5

$1 + l_{32} u_{23} + u_{33} = - 5$

$3 + u_{23} = - 3$

$u_{22} = - 2$

$1 + l_{32} u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.6

Reemplaza todos los casos de

$u_{22}$ por

$- 2$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.6.1

Mueve todos los términos que no contengan

$u_{23}$ al lado derecho de la ecuación.

Toca para ver más pasos...

Paso 3.2.6.1.1

Resta

$3$ de ambos lados de la ecuación.

$u_{23} = - 3 - 3$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$1 + l_{32} u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.6.1.2

Resta

$3$ de

$- 3$ .

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$1 + l_{32} u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$1 + l_{32} u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.6.2

Reemplaza todos los casos de

$u_{22}$ en

$1 + l_{32} u_{22} = - 2$ por

$- 2$ .

$1 + l_{32} \cdot - 2 = - 2$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.6.3

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.6.3.1

Mueve

$- 2$ a la izquierda de

$l_{32}$ .

$1 - 2 l_{32} = - 2$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$1 - 2 l_{32} = - 2$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$1 - 2 l_{32} = - 2$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7

Reemplaza todos los casos de

$u_{23}$ por

$- 6$ en cada ecuación.

Toca para ver más pasos...

Paso 3.2.7.1

Mueve todos los términos que no contengan

$l_{32}$ al lado derecho de la ecuación.

Toca para ver más pasos...

Paso 3.2.7.1.1

Resta

$1$ de ambos lados de la ecuación.

$- 2 l_{32} = - 2 - 1$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.1.2

Resta

$1$ de

$- 2$ .

$- 2 l_{32} = - 3$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$- 2 l_{32} = - 3$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.2

Divide cada término en

$- 2 l_{32} = - 3$ por

$- 2$ y simplifica.

Toca para ver más pasos...

Paso 3.2.7.2.1

Divide cada término en

$- 2 l_{32} = - 3$ por

$- 2$ .

$\frac{- 2 l_{32}}{- 2} = \frac{- 3}{- 2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.2.2

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.7.2.2.1

Cancela el factor común de

$- 2$ .

Toca para ver más pasos...

Paso 3.2.7.2.2.1.1

Cancela el factor común.

$\frac{- 2 l_{32}}{- 2} = \frac{- 3}{- 2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.2.2.1.2

Divide

$l_{32}$ por

$1$ .

$l_{32} = \frac{- 3}{- 2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$l_{32} = \frac{- 3}{- 2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$l_{32} = \frac{- 3}{- 2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.2.3

Simplifica el lado derecho.

Toca para ver más pasos...

Paso 3.2.7.2.3.1

La división de dos valores negativos da como resultado un valor positivo.

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$1 + l_{32} u_{23} + u_{33} = - 5$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.3

Reemplaza todos los casos de

$u_{23}$ en

$1 + l_{32} u_{23} + u_{33} = - 5$ por

$- 6$ .

$1 + l_{32} \cdot - 6 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.7.4

Simplifica el lado izquierdo.

Toca para ver más pasos...

Paso 3.2.7.4.1

Mueve

$- 6$ a la izquierda de

$l_{32}$ .

$1 - 6 l_{32} + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$1 - 6 l_{32} + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$1 - 6 l_{32} + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.8

Reemplaza todos los casos de

$l_{32}$ por

$\frac{3}{2}$ en cada ecuación.

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Paso 3.2.8.1

Reemplaza todos los casos de

$l_{32}$ en

$1 - 6 l_{32} + u_{33} = - 5$ por

$\frac{3}{2}$ .

$1 - 6 (\frac{3}{2}) + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.8.2

Simplifica el lado izquierdo.

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Paso 3.2.8.2.1

Simplifica

$1 - 6 (\frac{3}{2}) + u_{33}$ .

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Paso 3.2.8.2.1.1

Simplifica cada término.

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Paso 3.2.8.2.1.1.1

Cancela el factor común de

$2$ .

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Paso 3.2.8.2.1.1.1.1

Factoriza

$2$ de

$- 6$ .

$1 + 2 (- 3) (\frac{3}{2}) + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.8.2.1.1.1.2

Cancela el factor común.

$1 + 2 \cdot (- 3 (\frac{3}{2})) + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.8.2.1.1.1.3

Reescribe la expresión.

$1 - 3 \cdot 3 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$1 - 3 \cdot 3 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.8.2.1.1.2

Multiplica

$- 3$ por

$3$ .

$1 - 9 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$1 - 9 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.8.2.1.2

Resta

$9$ de

$1$ .

$- 8 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$- 8 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$- 8 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$- 8 + u_{33} = - 5$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.9

Mueve todos los términos que no contengan

$u_{33}$ al lado derecho de la ecuación.

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Paso 3.2.9.1

Suma

$8$ a ambos lados de la ecuación.

$u_{33} = - 5 + 8$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.9.2

Suma

$- 5$ y

$8$ .

$u_{33} = 3$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

$u_{33} = 3$

$l_{32} = \frac{3}{2}$

$u_{23} = - 6$

$u_{22} = - 2$

$l_{31} = 1$

$l_{21} = 3$

$u_{11} = 1$

$u_{12} = 1$

$u_{13} = 1$

Paso 3.2.10

Resuelve el sistema de ecuaciones.

$u_{33} = 3 l_{32} = \frac{3}{2} u_{23} = - 6 u_{22} = - 2 l_{31} = 1 l_{21} = 3 u_{11} = 1 u_{12} = 1 u_{13} = 1$

Paso 3.2.11

Enumera todas las soluciones.

$u_{33} = 3, l_{32} = \frac{3}{2}, u_{23} = - 6, u_{22} = - 2, l_{31} = 1, l_{21} = 3, u_{11} = 1, u_{12} = 1, u_{13} = 1$

Paso 4

Sustituye en los valores resueltos.

$[\begin{array}{c} 1 & 1 & 1 \\ 3 & 1 & - 3 \\ 1 & - 2 & - 5 \end{array}] = [\begin{array}{c} 1 & 0 & 0 \\ 3 & 1 & 0 \\ 1 & \frac{3}{2} & 1 \end{array}] [\begin{array}{c} 1 & 1 & 1 \\ 0 & - 2 & - 6 \\ 0 & 0 & 3 \end{array}]$

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