Solve the Matrix Equation x+[[6,1],[-2,3]]=[[2,0],[-3,1]]

$x + [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}] = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}]$

Step 1

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}] = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 6 - 6 & 1 - 1 \\ - 2 - (- 2) & 3 - 3 \end{array}] + X = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 6 - 6 & 1 - 1 \\ - 2 - (- 2) & 3 - 3 \end{array}]$ .

Simplify $6 - 6$ .

$[\begin{array}{c} 0 & 1 - 1 \\ - 2 - (- 2) & 3 - 3 \end{array}] + X = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}]$

Simplify $1 - 1$ .

$[\begin{array}{c} 0 & 0 \\ - 2 - (- 2) & 3 - 3 \end{array}] + X = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}]$

Simplify $- 2 - (- 2)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 3 - 3 \end{array}] + X = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}]$

Simplify $3 - 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & 0 \\ - 3 & 1 \end{array}] - [\begin{array}{c} 6 & 1 \\ - 2 & 3 \end{array}]$

Simplify the right side of the equation.

Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 - 6 & 0 - 1 \\ - 3 - (- 2) & 1 - 3 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 6 & 0 - 1 \\ - 3 - (- 2) & 1 - 3 \end{array}]$ .

Simplify $2 - 6$ .

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

Simplify $0 - 1$ .

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

Simplify $- 3 - (- 2)$ .

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

Simplify $1 - 3$ .

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

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

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

Step 3

The matrix is in the most simplified form.

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

Solve the Matrix Equation x+[[6,1],[-2,3]]=[[2,0],[-3,1]]

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