Solve the Matrix Equation [[4,7],[1,2]]X+[[2,7],[-3,4]]=[[6,2],[-2,3]]

$[\begin{array}{c} 4 & 7 \\ 1 & 2 \end{array}] X + [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}] = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$X \cdot X + [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}] = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Multiply $X$ by $X$ .

$[\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}] + X^{2} = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Subtract the corresponding elements.

$[\begin{array}{c} 2 - 2 & 7 - 7 \\ - 3 - (- 3) & 4 - 4 \end{array}] + X^{2} = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 2 & 7 - 7 \\ - 3 - (- 3) & 4 - 4 \end{array}]$ .

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 7 - 7 \\ - 3 - (- 3) & 4 - 4 \end{array}] + X^{2} = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Simplify $7 - 7$ .

$[\begin{array}{c} 0 & 0 \\ - 3 - (- 3) & 4 - 4 \end{array}] + X^{2} = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Simplify $- 3 - (- 3)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 4 - 4 \end{array}] + X^{2} = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X^{2} = [\begin{array}{c} 6 & 2 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 2 & 7 \\ - 3 & 4 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X^{2} = [\begin{array}{c} 6 - 2 & 2 - 7 \\ - 2 - (- 3) & 3 - 4 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 6 - 2 & 2 - 7 \\ - 2 - (- 3) & 3 - 4 \end{array}]$ .

Simplify $6 - 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X^{2} = [\begin{array}{c} 4 & 2 - 7 \\ - 2 - (- 3) & 3 - 4 \end{array}]$

Simplify $2 - 7$ .

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

Simplify $- 2 - (- 3)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X^{2} = [\begin{array}{c} 4 & - 5 \\ 1 & 3 - 4 \end{array}]$

Simplify $3 - 4$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X^{2} = [\begin{array}{c} 4 & - 5 \\ 1 & - 1 \end{array}]$

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

$X^{2} = [\begin{array}{c} 4 & - 5 \\ 1 & - 1 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X^{2} = [\begin{array}{c} 4 & - 5 \\ 1 & - 1 \end{array}]$

Solve the Matrix Equation [[4,7],[1,2]]X+[[2,7],[-3,4]]=[[6,2],[-2,3]]

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