Solve the Matrix Equation x-[[-20,10],[3,14]]=[[13,18],[1,19]]

$x - [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}] = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}]$

Step 1

Add the matrix to both sides of the equation.

$X - [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}] = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Add the corresponding elements.

$[\begin{array}{c} 20 - 20 & - 10 + 10 \\ - 3 + 3 & - 14 + 14 \end{array}] + X = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 20 - 20 & - 10 + 10 \\ - 3 + 3 & - 14 + 14 \end{array}]$ .

Simplify $20 - 20$ .

$[\begin{array}{c} 0 & - 10 + 10 \\ - 3 + 3 & - 14 + 14 \end{array}] + X = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}]$

Simplify $- 10 + 10$ .

$[\begin{array}{c} 0 & 0 \\ - 3 + 3 & - 14 + 14 \end{array}] + X = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}]$

Simplify $- 3 + 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & - 14 + 14 \end{array}] + X = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}]$

Simplify $- 14 + 14$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 & 18 \\ 1 & 19 \end{array}] + [\begin{array}{c} - 20 & 10 \\ 3 & 14 \end{array}]$

Simplify the right side of the equation.

Add the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 13 - 20 & 18 + 10 \\ 1 + 3 & 19 + 14 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 13 - 20 & 18 + 10 \\ 1 + 3 & 19 + 14 \end{array}]$ .

Simplify $13 - 20$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 7 & 18 + 10 \\ 1 + 3 & 19 + 14 \end{array}]$

Simplify $18 + 10$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 7 & 28 \\ 1 + 3 & 19 + 14 \end{array}]$

Simplify $1 + 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 7 & 28 \\ 4 & 19 + 14 \end{array}]$

Simplify $19 + 14$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 7 & 28 \\ 4 & 33 \end{array}]$

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

$X = [\begin{array}{c} - 7 & 28 \\ 4 & 33 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} - 7 & 28 \\ 4 & 33 \end{array}]$

Solve the Matrix Equation x-[[-20,10],[3,14]]=[[13,18],[1,19]]

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