Algebra Examples

$x + [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}]$

Subtract $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ from both sides of the equation.

$X + [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}] = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify both sides of the equation.

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

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Subtract $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ from $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ by subtracting the corresponding elements of $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ from each element of $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ .

$[\begin{array}{c} 1 - 1 & 0 - 0 \\ 0 - 0 & 1 - 1 \end{array}] + X = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify element $0, 0$ of the matrix.

$[\begin{array}{c} 0 & 0 - 0 \\ 0 - 0 & 1 - 1 \end{array}] + X = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify element $0, 1$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 - 0 & 1 - 1 \end{array}] + X = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify element $1, 0$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 & 1 - 1 \end{array}] + X = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify element $1, 1$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify the right side of the equation.

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Combine the similar matrices with each others.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}] - [\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$

Simplify each element of the matrix $[\begin{array}{c} 2 - 1 & - 2 - 0 \\ 9 - 0 & - 9 - 1 \end{array}]$ .

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Subtract $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ from $[\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}]$ by subtracting the corresponding elements of $[\begin{array}{c} 1 & 0 \\ 0 & 1 \end{array}]$ from each element of $[\begin{array}{c} 2 & - 2 \\ 9 & - 9 \end{array}]$ .

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 2 - 1 & - 2 - 0 \\ 9 - 0 & - 9 - 1 \end{array}]$

Simplify element $0, 0$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 1 & - 2 - 0 \\ 9 - 0 & - 9 - 1 \end{array}]$

Simplify element $0, 1$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 1 & - 2 \\ 9 - 0 & - 9 - 1 \end{array}]$

Simplify element $1, 0$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 1 & - 2 \\ 9 & - 9 - 1 \end{array}]$

Simplify element $1, 1$ of the matrix.

$[\begin{array}{c} 0 & 0 \\ 0 & 0 \end{array}] + X = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]$

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

$X = [\begin{array}{c} 1 & - 2 \\ 9 & - 10 \end{array}]$

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