Solve the Matrix Equation 2[[-5,-2],[0,7]]=[[-10,x],[0,14]]

$2 [\begin{array}{c} - 5 & - 2 \\ 0 & 7 \end{array}] = [\begin{array}{c} - 10 & x \\ 0 & 14 \end{array}]$

Step 1

Simplify the left side of the equation.

Multiply $2$ by each element of the matrix.

$[\begin{array}{c} 2 \cdot - 5 & 2 \cdot - 2 \\ 2 \cdot 0 & 2 \cdot 7 \end{array}] = [\begin{array}{c} - 10 & x \\ 0 & 14 \end{array}]$

Simplify each element in the matrix.

Rearrange $2 \cdot - 5$ .

$[\begin{array}{c} - 10 & 2 \cdot - 2 \\ 2 \cdot 0 & 2 \cdot 7 \end{array}] = [\begin{array}{c} - 10 & x \\ 0 & 14 \end{array}]$

Rearrange $2 \cdot - 2$ .

$[\begin{array}{c} - 10 & - 4 \\ 2 \cdot 0 & 2 \cdot 7 \end{array}] = [\begin{array}{c} - 10 & x \\ 0 & 14 \end{array}]$

Rearrange $2 \cdot 0$ .

$[\begin{array}{c} - 10 & - 4 \\ 0 & 2 \cdot 7 \end{array}] = [\begin{array}{c} - 10 & x \\ 0 & 14 \end{array}]$

Rearrange $2 \cdot 7$ .

$[\begin{array}{c} - 10 & - 4 \\ 0 & 14 \end{array}] = [\begin{array}{c} - 10 & x \\ 0 & 14 \end{array}]$

Step 2

The matrix equation can be written as a set of equations.

$- 10 = - 10$

$- 4 = x$

$0 = 0$

$14 = 14$

Step 3

Rewrite the equation as $x = - 4$ .

$x = - 4$