Find the Variables [[x],[y]]=[[-2,5],[1,-2]][[-1],[2]]

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 2 & 5 \\ 1 & - 2 \end{array}] [\begin{array}{c} - 1 \\ 2 \end{array}]$

Step 1

Simplify the right side of the equation.

Multiply each row in the first matrix by each column in the second matrix.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} - 2 \cdot - 1 + 5 \cdot 2 \\ 1 \cdot - 1 - 2 \cdot 2 \end{array}]$

Simplify each element of the matrix by multiplying out all the expressions.

$[\begin{array}{c} x \\ y \end{array}] = [\begin{array}{c} 12 \\ - 5 \end{array}]$

Step 2

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

$x = 12$

$y = - 5$

Step 3

The system is already solved.

$x = 12, y = - 5$