Solve the Matrix Equation [[4,-5],[9,-2]]+x=[[6,3],[2,11]]

$[\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}] + x = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$[\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}] + X - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}] = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}] - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 4 - 4 & - 5 - (- 5) \\ 9 - 9 & - 2 - (- 2) \end{array}] + X = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}] - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 4 - 4 & - 5 - (- 5) \\ 9 - 9 & - 2 - (- 2) \end{array}]$ .

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & - 5 - (- 5) \\ 9 - 9 & - 2 - (- 2) \end{array}] + X = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}] - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}]$

Simplify $- 5 - (- 5)$ .

$[\begin{array}{c} 0 & 0 \\ 9 - 9 & - 2 - (- 2) \end{array}] + X = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}] - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}]$

Simplify $9 - 9$ .

$[\begin{array}{c} 0 & 0 \\ 0 & - 2 - (- 2) \end{array}] + X = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}] - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}]$

Simplify $- 2 - (- 2)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 6 & 3 \\ 2 & 11 \end{array}] - [\begin{array}{c} 4 & - 5 \\ 9 & - 2 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 6 - 4 & 3 - (- 5) \\ 2 - 9 & 11 - (- 2) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 6 - 4 & 3 - (- 5) \\ 2 - 9 & 11 - (- 2) \end{array}]$ .

Simplify $6 - 4$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 3 - (- 5) \\ 2 - 9 & 11 - (- 2) \end{array}]$

Simplify $3 - (- 5)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 8 \\ 2 - 9 & 11 - (- 2) \end{array}]$

Simplify $2 - 9$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 8 \\ - 7 & 11 - (- 2) \end{array}]$

Simplify $11 - (- 2)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 8 \\ - 7 & 13 \end{array}]$

Adding the null matrix to any matrix is a matrix itself.

$X = [\begin{array}{c} 2 & 8 \\ - 7 & 13 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} 2 & 8 \\ - 7 & 13 \end{array}]$

Solve the Matrix Equation [[4,-5],[9,-2]]+x=[[6,3],[2,11]]

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