Solve the Matrix Equation x+[[20,10],[-12,3]]=[[23,16],[24,11]]

$x + [\begin{array}{c} 20 & 10 \\ - 12 & 3 \end{array}] = [\begin{array}{c} 23 & 16 \\ 24 & 11 \end{array}]$

Step 1

Move all terms not containing a variable to the right side.

Subtract $[\begin{array}{c} 20 & 10 \\ - 12 & 3 \end{array}]$ from both sides of the equation.

$x = [\begin{array}{c} 23 & 16 \\ 24 & 11 \end{array}] - [\begin{array}{c} 20 & 10 \\ - 12 & 3 \end{array}]$

Step 2

Simplify the right side.

Subtract the corresponding elements.

$x = [\begin{array}{c} 23 - 20 & 16 - 10 \\ 24 + 12 & 11 - 3 \end{array}]$

Simplify each element.

Subtract $20$ from $23$ .

$x = [\begin{array}{c} 3 & 16 - 10 \\ 24 + 12 & 11 - 3 \end{array}]$

Subtract $10$ from $16$ .

$x = [\begin{array}{c} 3 & 6 \\ 24 + 12 & 11 - 3 \end{array}]$

Add $24$ and $12$ .

$x = [\begin{array}{c} 3 & 6 \\ 36 & 11 - 3 \end{array}]$

Subtract $3$ from $11$ .

$x = [\begin{array}{c} 3 & 6 \\ 36 & 8 \end{array}]$