Algebra Examples

$x - [\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}] = [\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}]$

Add $[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$ to both sides of the equation.

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

Simplify both sides of the equation.

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

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Combine the same size matrices $[\begin{array}{c} - 1 & 1 & 0 \\ 0 & - 1 & - 1 \end{array}]$ and $[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$ by adding the corresponding elements of each.

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

Simplify element $0, 0$ of the matrix.

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

Simplify element $0, 1$ of the matrix.

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

Simplify element $0, 2$ of the matrix.

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

Simplify element $1, 0$ of the matrix.

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

Simplify element $1, 1$ of the matrix.

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

Simplify element $1, 2$ of the matrix.

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

Simplify the right side of the equation.

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Combine the similar matrices with each others.

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

Simplify each element of the matrix $[\begin{array}{c} 1 + 2 & - 1 + 2 & 0 + 2 \\ 0 + 8 & 1 + 3 & 1 + 4 \end{array}]$ .

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Combine the same size matrices $[\begin{array}{c} 2 & 2 & 2 \\ 8 & 3 & 4 \end{array}]$ and $[\begin{array}{c} 1 & - 1 & 0 \\ 0 & 1 & 1 \end{array}]$ by adding the corresponding elements of each.

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

Simplify element $0, 0$ of the matrix.

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

Simplify element $0, 1$ of the matrix.

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

Simplify element $0, 2$ of the matrix.

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

Simplify element $1, 0$ of the matrix.

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

Simplify element $1, 1$ of the matrix.

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

Simplify element $1, 2$ of the matrix.

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] + X = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

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

$X = [\begin{array}{c} 3 & 1 & 2 \\ 8 & 4 & 5 \end{array}]$

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