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

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

Step 1

Subtract the matrix from both sides of the equation.

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

Step 2

Simplify both sides of the equation.

Simplify the left side of the equation.

Subtract the corresponding elements.

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

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

Simplify $4 - 4$ .

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

Simplify $2 - 2$ .

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

Simplify $3 - 3$ .

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

Simplify $5 - 5$ .

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

Simplify the right side of the equation.

Subtract the corresponding elements.

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

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

Simplify $3 - 4$ .

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

Simplify $- 4 - 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 1 & - 6 \\ 4 - 3 & - 5 - 5 \end{array}]$

Simplify $4 - 3$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 1 & - 6 \\ 1 & - 5 - 5 \end{array}]$

Simplify $- 5 - 5$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 1 & - 6 \\ 1 & - 10 \end{array}]$

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

$X = [\begin{array}{c} - 1 & - 6 \\ 1 & - 10 \end{array}]$

Step 3

The matrix is in the most simplified form.

$X = [\begin{array}{c} - 1 & - 6 \\ 1 & - 10 \end{array}]$

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

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