Algebra Examples

$- 8 [\begin{array}{c} 2 & 11 & 4 \\ 0 & 2 & - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 1

Multiply $- 8$ by each element of the matrix.

$[\begin{array}{c} - 8 \cdot 2 & - 8 \cdot 11 & - 8 \cdot 4 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $- 8$ by $2$ .

$[\begin{array}{c} - 16 & - 8 \cdot 11 & - 8 \cdot 4 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2.2

Multiply $- 8$ by $11$ .

$[\begin{array}{c} - 16 & - 88 & - 8 \cdot 4 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2.3

Multiply $- 8$ by $4$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ - 8 \cdot 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2.4

Multiply $- 8$ by $0$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ 0 & - 8 \cdot 2 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2.5

Multiply $- 8$ by $2$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ 0 & - 16 & - 8 \cdot - 6 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 2.6

Multiply $- 8$ by $- 6$ .

$[\begin{array}{c} - 16 & - 88 & - 32 \\ 0 & - 16 & 48 \end{array}] = [\begin{array}{c} - 16 & - 88 & x \\ 0 & - 16 & 48 \end{array}]$

Step 3

Write as a linear system of equations.

$- 16 = - 16$

$- 88 = - 88$

$- 32 = x$

$0 = 0$

$- 16 = - 16$

$48 = 48$

Step 4

Since $48 = 48$ is always true, the matrix equation has infinite solutions.

Infinite solutions satisfying $- 32 = x$ .