Algebra Examples

$x + [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}] = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}]$

Subtract the matrix from both sides of the equation.

$X + [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}] = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}]$

Simplify both sides of the equation.

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Simplify the left side of the equation.

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Subtract the corresponding elements.

$[\begin{array}{c} - 3 - (- 3) & 2 - 2 \\ 9 - 9 & - 7 - (- 7) \end{array}] + X = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 3 - (- 3) & 2 - 2 \\ 9 - 9 & - 7 - (- 7) \end{array}]$ .

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Simplify $- 3 - (- 3)$ .

$[\begin{array}{c} 0 & 2 - 2 \\ 9 - 9 & - 7 - (- 7) \end{array}] + X = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}]$

Simplify $2 - 2$ .

$[\begin{array}{c} 0 & 0 \\ 9 - 9 & - 7 - (- 7) \end{array}] + X = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}]$

Simplify $9 - 9$ .

$[\begin{array}{c} 0 & 0 \\ 0 & - 7 - (- 7) \end{array}] + X = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}]$

Simplify $- 7 - (- 7)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 3 & 5 \\ 4 & - 5 \end{array}] - [\begin{array}{c} - 3 & 2 \\ 9 & - 7 \end{array}]$

Simplify the right side of the equation.

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Subtract the corresponding elements.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} - 3 - (- 3) & 5 - 2 \\ 4 - 9 & - 5 - (- 7) \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} - 3 - (- 3) & 5 - 2 \\ 4 - 9 & - 5 - (- 7) \end{array}]$ .

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Simplify $- 3 - (- 3)$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 0 & 5 - 2 \\ 4 - 9 & - 5 - (- 7) \end{array}]$

Simplify $5 - 2$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 0 & 3 \\ 4 - 9 & - 5 - (- 7) \end{array}]$

Simplify $4 - 9$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 0 & 3 \\ - 5 & - 5 - (- 7) \end{array}]$

Simplify $- 5 - (- 7)$ .

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

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

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

The matrix is in the most simplified form.

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