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$[\begin{array}{c} a + 7 & 12 z + 1 & 8 m \\ 12 k & 1 & 5 \end{array}] + [\begin{array}{c} 12 a & 9 z & 10 m \\ 6 k & 4 & 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 1

اجمع العناصر المتناظرة.

$[\begin{array}{c} a + 7 + 12 a & 12 z + 1 + 9 z & 8 m + 10 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 2

Simplify each element.

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خطوة 2.1

أضف $a$ و $12 a$ .

$[\begin{array}{c} 13 a + 7 & 12 z + 1 + 9 z & 8 m + 10 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 2.2

أضف $12 z$ و $9 z$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 8 m + 10 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 2.3

أضف $8 m$ و $10 m$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 12 k + 6 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 2.4

أضف $12 k$ و $6 k$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 18 k & 1 + 4 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 2.5

أضف $1$ و $4$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 18 k & 5 & 5 + 5 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 2.6

أضف $5$ و $5$ .

$[\begin{array}{c} 13 a + 7 & 21 z + 1 & 18 m \\ 18 k & 5 & 10 \end{array}] = [\begin{array}{c} 33 & - 104 & 108 \\ 54 & 5 & 10 \end{array}]$

خطوة 3

Write as a linear system of equations.

$13 a + 7 = 33$

$21 z + 1 = - 104$

$18 m = 108$

$18 k = 54$

$5 = 5$

$10 = 10$

خطوة 4

Since $10 = 10$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying the system.