Álgebra lineal Ejemplos

x - [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}] = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}]

$x - [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}] = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}]$

Paso 1

Move all terms not containing a variable to the right side.

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Paso 1.1

Suma

[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]

$[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$ a ambos lados de la ecuación.

x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]

$x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$

x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]

$x = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}] + [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$

Paso 2

Simplifica el lado derecho.

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Paso 2.1

Suma los elementos correspondientes.

x = [\begin{array}{c} 2 + 1 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 2 + 1 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Paso 2.2

Simplify each element.

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Paso 2.2.1

Suma

2

$2$ y

1

$1$ .

x = [\begin{array}{c} 3 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 2 - 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Paso 2.2.2

Resta

1

$1$ de

2

$2$ .

x = [\begin{array}{c} 3 & 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 + 0 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Paso 2.2.3

Suma

2

$2$ y

0

$0$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 + 0 & 3 + 1 & 4 + 1 \end{array}]$

Paso 2.2.4

Suma

8

$8$ y

0

$0$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 3 + 1 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 3 + 1 & 4 + 1 \end{array}]$

Paso 2.2.5

Suma

3

$3$ y

1

$1$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 4 + 1 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 4 + 1 \end{array}]$

Paso 2.2.6

Suma

4

$4$ y

1

$1$ .

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]

$x = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

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