Álgebra linear Exemplos

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}] - [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 1

Combine os termos opostos em $[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}] - [\begin{array}{c} 3 & 2 \\ 1 & 0 \end{array}]$ .

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Etapa 1.1

Subtraia os elementos correspondentes.

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 3 - 3 & 2 - 2 \\ 1 - 1 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 1.2

Simplify each element.

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Etapa 1.2.1

Subtraia $3$ de $3$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 2 - 2 \\ 1 - 1 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 1.2.2

Subtraia $2$ de $2$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 0 \\ 1 - 1 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 1.2.3

Subtraia $1$ de $1$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 0 \\ 0 & 0 - 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 1.2.4

Subtraia $0$ de $0$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] + [\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 2

Adding any matrix to a null matrix is the matrix itself.

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Etapa 2.1

Adicione os elementos correspondentes.

$[\begin{array}{c} x + 0 & y + 0 \\ w + 0 & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 2.2

Simplify each element.

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Etapa 2.2.1

Some $x$ e $0$ .

$[\begin{array}{c} x & y + 0 \\ w + 0 & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 2.2.2

Some $y$ e $0$ .

$[\begin{array}{c} x & y \\ w + 0 & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 2.2.3

Some $w$ e $0$ .

$[\begin{array}{c} x & y \\ w & z + 0 \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 2.2.4

Some $z$ e $0$ .

$[\begin{array}{c} x & y \\ w & z \end{array}] = [\begin{array}{c} 6 & 3 \\ 7 & - 1 \end{array}]$

Etapa 3

Write as a linear system of equations.

$x = 6$

$y = 3$

$w = 7$

$z = - 1$

Etapa 4

O sistema já foi resolvido.

$x = 6, y = 3, w = 7, z = - 1$