Solve the Matrix Equation x-[[3,4],[-5,2]]=[[5,-1],[1,0]]

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

Add the matrix to both sides of the equation.

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

Simplify both sides of the equation.

Simplify the left side of the equation.

Add the corresponding elements.

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

Simplify each element of the matrix $[\begin{array}{c} - 3 + 3 & - 4 + 4 \\ 5 - 5 & - 2 + 2 \end{array}]$ .

Simplify $- 3 + 3$ .

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

Simplify $- 4 + 4$ .

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

Simplify $5 - 5$ .

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

Simplify $- 2 + 2$ .

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

Simplify the right side of the equation.

Add the corresponding elements.

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

Simplify each element of the matrix $[\begin{array}{c} 5 + 3 & - 1 + 4 \\ 1 - 5 & 0 + 2 \end{array}]$ .

Simplify $5 + 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & - 1 + 4 \\ 1 - 5 & 0 + 2 \end{array}]$

Simplify $- 1 + 4$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & 3 \\ 1 - 5 & 0 + 2 \end{array}]$

Simplify $1 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & 3 \\ - 4 & 0 + 2 \end{array}]$

Simplify $0 + 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 8 & 3 \\ - 4 & 2 \end{array}]$

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

$X = [\begin{array}{c} 8 & 3 \\ - 4 & 2 \end{array}]$

The matrix is in the most simplified form.

$X = [\begin{array}{c} 8 & 3 \\ - 4 & 2 \end{array}]$

Solve the Matrix Equation x-[[3,4],[-5,2]]=[[5,-1],[1,0]]

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