Álgebra linear Exemplos

$[\begin{array}{c} 11 & - 8 \\ - 17 & - 11 \\ 8 & - 12 \\ - 2 x & 3 \end{array}] + [\begin{array}{c} - 3 & 3 \\ - 17 & 12 \\ - 19 & 8 \\ - 15 & 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 1

Adicione os elementos correspondentes.

$[\begin{array}{c} 11 - 3 & - 8 + 3 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2

Simplify each element.

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Etapa 2.1

Subtraia $3$ de $11$ .

$[\begin{array}{c} 8 & - 8 + 3 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2.2

Some $- 8$ e $3$ .

$[\begin{array}{c} 8 & - 5 \\ - 17 - 17 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2.3

Subtraia $17$ de $- 17$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & - 11 + 12 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2.4

Some $- 11$ e $12$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ 8 - 19 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2.5

Subtraia $19$ de $8$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 12 + 8 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2.6

Some $- 12$ e $8$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 4 \\ - 2 x - 15 & 3 + 2 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 2.7

Some $3$ e $2$ .

$[\begin{array}{c} 8 & - 5 \\ - 34 & 1 \\ - 11 & - 4 \\ - 2 x - 15 & 5 \end{array}] - [\begin{array}{c} - 13 & 18 \\ 11 & - 16 \\ 0 & - 18 \\ 13 & - 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 3

Subtraia os elementos correspondentes.

$[\begin{array}{c} 8 + 13 & - 5 - 18 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4

Simplify each element.

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Etapa 4.1

Some $8$ e $13$ .

$[\begin{array}{c} 21 & - 5 - 18 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.2

Subtraia $18$ de $- 5$ .

$[\begin{array}{c} 21 & - 23 \\ - 34 - 11 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.3

Subtraia $11$ de $- 34$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 1 + 16 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.4

Some $1$ e $16$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 - 0 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.5

Subtraia $0$ de $- 11$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & - 4 + 18 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.6

Some $- 4$ e $18$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 15 - 13 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.7

Subtraia $13$ de $- 15$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 28 & 5 + 7 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 4.8

Some $5$ e $7$ .

$[\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 2 x - 28 & 12 \end{array}] = [\begin{array}{c} 21 & - 23 \\ - 45 & 17 \\ - 11 & 14 \\ - 24 & 12 \end{array}]$

Etapa 5

Write as a linear system of equations.

$21 = 21$

$- 23 = - 23$

$- 45 = - 45$

$17 = 17$

$- 11 = - 11$

$14 = 14$

$- 2 x - 28 = - 24$

$12 = 12$

Etapa 6

Since $12 = 12$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 2 x - 28 = - 24$ .