Matemática discreta Ejemplos

$- x + 3 y = 11$ , $3 x - 9 y = - 30$

Paso 1

Write the system as a matrix.

$[\begin{array}{c} - 1 & 3 & 11 \\ 3 & - 9 & - 30 \end{array}]$

Paso 2

Obtén la forma escalonada reducida por filas.

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Paso 2.1

Multiply each element of $R_{1}$ by $- 1$ to make the entry at $1, 1$ a $1$ .

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Paso 2.1.1

Multiply each element of $R_{1}$ by $- 1$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} - - 1 & - 1 \cdot 3 & - 1 \cdot 11 \\ 3 & - 9 & - 30 \end{array}]$

Paso 2.1.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & - 3 & - 11 \\ 3 & - 9 & - 30 \end{array}]$

Paso 2.2

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

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Paso 2.2.1

Perform the row operation $R_{2} = R_{2} - 3 R_{1}$ to make the entry at $2, 1$ a $0$ .

$[\begin{array}{c} 1 & - 3 & - 11 \\ 3 - 3 \cdot 1 & - 9 - 3 \cdot - 3 & - 30 - 3 \cdot - 11 \end{array}]$

Paso 2.2.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - 3 & - 11 \\ 0 & 0 & 3 \end{array}]$

Paso 2.3

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 3$ a $1$ .

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Paso 2.3.1

Multiply each element of $R_{2}$ by $\frac{1}{3}$ to make the entry at $2, 3$ a $1$ .

$[\begin{array}{c} 1 & - 3 & - 11 \\ \frac{0}{3} & \frac{0}{3} & \frac{3}{3} \end{array}]$

Paso 2.3.2

Simplifica $R_{2}$ .

$[\begin{array}{c} 1 & - 3 & - 11 \\ 0 & 0 & 1 \end{array}]$

Paso 2.4

Perform the row operation $R_{1} = R_{1} + 11 R_{2}$ to make the entry at $1, 3$ a $0$ .

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Paso 2.4.1

Perform the row operation $R_{1} = R_{1} + 11 R_{2}$ to make the entry at $1, 3$ a $0$ .

$[\begin{array}{c} 1 + 11 \cdot 0 & - 3 + 11 \cdot 0 & - 11 + 11 \cdot 1 \\ 0 & 0 & 1 \end{array}]$

Paso 2.4.2

Simplifica $R_{1}$ .

$[\begin{array}{c} 1 & - 3 & 0 \\ 0 & 0 & 1 \end{array}]$

Paso 3

Use the result matrix to declare the final solution to the system of equations.

$x - 3 y = 0$

$0 = 1$

Paso 4

The system is inconsistent so there is no solution.

$No hay solución$