Solve the Matrix Equation x-[[1,-19,3],[16,-4,8]]=[[1,-14,3],[12,-19,1]]

$x - [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}] = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}]$

Step 1

Add the matrix to both sides of the equation.

$X - [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}] = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Add the corresponding elements.

$[\begin{array}{c} - 1 + 1 & 19 - 19 & - 3 + 3 \\ - 16 + 16 & 4 - 4 & - 8 + 8 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 1 + 1 & 19 - 19 & - 3 + 3 \\ - 16 + 16 & 4 - 4 & - 8 + 8 \end{array}]$ .

Simplify $- 1 + 1$ .

$[\begin{array}{c} 0 & 19 - 19 & - 3 + 3 \\ - 16 + 16 & 4 - 4 & - 8 + 8 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify $19 - 19$ .

$[\begin{array}{c} 0 & 0 & - 3 + 3 \\ - 16 + 16 & 4 - 4 & - 8 + 8 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify $- 3 + 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ - 16 + 16 & 4 - 4 & - 8 + 8 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify $- 16 + 16$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 4 - 4 & - 8 + 8 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify $4 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & - 8 + 8 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify $- 8 + 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 1 & - 14 & 3 \\ 12 & - 19 & 1 \end{array}] + [\begin{array}{c} 1 & - 19 & 3 \\ 16 & - 4 & 8 \end{array}]$

Simplify the right side of the equation.

Add the corresponding elements.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 1 + 1 & - 14 - 19 & 3 + 3 \\ 12 + 16 & - 19 - 4 & 1 + 8 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 1 + 1 & - 14 - 19 & 3 + 3 \\ 12 + 16 & - 19 - 4 & 1 + 8 \end{array}]$ .

Simplify $1 + 1$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 14 - 19 & 3 + 3 \\ 12 + 16 & - 19 - 4 & 1 + 8 \end{array}]$

Simplify $- 14 - 19$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 33 & 3 + 3 \\ 12 + 16 & - 19 - 4 & 1 + 8 \end{array}]$

Simplify $3 + 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 33 & 6 \\ 12 + 16 & - 19 - 4 & 1 + 8 \end{array}]$

Simplify $12 + 16$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 33 & 6 \\ 28 & - 19 - 4 & 1 + 8 \end{array}]$

Simplify $- 19 - 4$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 33 & 6 \\ 28 & - 23 & 1 + 8 \end{array}]$

Simplify $1 + 8$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 33 & 6 \\ 28 & - 23 & 9 \end{array}]$

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

$X = [\begin{array}{c} 2 & - 33 & 6 \\ 28 & - 23 & 9 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} 2 & - 33 & 6 \\ 28 & - 23 & 9 \end{array}]$

Solve the Matrix Equation x-[[1,-19,3],[16,-4,8]]=[[1,-14,3],[12,-19,1]]

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