Algebra Examples

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

Step 1

Add the matrix to both sides of the equation.

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

Step 2

Simplify both sides of the equation.

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Simplify the left side of the equation.

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Add the corresponding elements.

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

Simplify 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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Simplify $- 1 + 1$ .

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

Simplify $1 - 1$ .

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

Simplify $0 + 0$ .

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

Simplify $0 + 0$ .

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

Simplify $- 1 + 1$ .

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

Simplify $- 1 + 1$ .

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

Simplify the right side of the equation.

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Add the corresponding elements.

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

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

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Simplify $2 + 1$ .

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

Simplify $2 - 1$ .

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

Simplify $2 + 0$ .

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

Simplify $8 + 0$ .

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

Simplify $3 + 1$ .

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

Simplify $4 + 1$ .

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

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

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

Step 3

The matrix is in the most simplified form.

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

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