Álgebra linear Exemplos

$[\begin{array}{c} 8 & 9 \end{array}]$

Etapa 1

Write as an augmented matrix for $A x = 0$ .

$[\begin{array}{c} 8 & 9 & 0 \end{array}]$

Etapa 2

Encontre a forma escalonada reduzida por linhas.

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Etapa 2.1

Multiply each element of $R_{1}$ by $\frac{1}{8}$ to make the entry at $1, 1$ a $1$ .

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Etapa 2.1.1

Multiply each element of $R_{1}$ by $\frac{1}{8}$ to make the entry at $1, 1$ a $1$ .

$[\begin{array}{c} \frac{8}{8} & \frac{9}{8} & \frac{0}{8} \end{array}]$

Etapa 2.1.2

Simplifique $R_{1}$ .

$[\begin{array}{c} 1 & \frac{9}{8} & 0 \end{array}]$

Etapa 3

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

$x + \frac{9}{8} y = 0$

Etapa 4

Write a solution vector by solving in terms of the free variables in each row.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - \frac{9 y}{8} \\ y \end{array}]$

Etapa 5

Write the solution as a linear combination of vectors.

$[\begin{array}{c} x \\ y \end{array}] = y [\begin{array}{c} - \frac{9}{8} \\ 1 \end{array}]$

Etapa 6

Write as a solution set.

${y [\begin{array}{c} - \frac{9}{8} \\ 1 \end{array}] | y \in R}$