Solve [[2,-2,3],[-3,-3,4]]-x=[[2,2,0],[1,-1,-1]]

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

Subtract $[\begin{array}{c} 2 & - 2 & 3 \\ - 3 & - 3 & 4 \end{array}]$ from both sides of the equation.

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

Simplify both sides of the equation.

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Simplify the left side of the equation.

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Can’t combine different size matrices.

Subtract the corresponding elements of $[\begin{array}{c} 2 & - 2 & 3 \\ - 3 & - 3 & 4 \end{array}]$ from each element of $[\begin{array}{c} 2 & - 2 & 3 \\ - 3 & - 3 & 4 \end{array}]$ .

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

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

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Simplify $2 - 2$ .

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

Simplify $- 2 - (- 2)$ .

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

Simplify $3 - 3$ .

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

Simplify $- 3 - (- 3)$ .

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

Simplify $- 3 - (- 3)$ .

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

Simplify $4 - 4$ .

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

Simplify the right side of the equation.

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Subtract the corresponding elements of $[\begin{array}{c} 2 & - 2 & 3 \\ - 3 & - 3 & 4 \end{array}]$ from each element of $[\begin{array}{c} 2 & 2 & 0 \\ 1 & - 1 & - 1 \end{array}]$ .

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

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

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Simplify $2 - 2$ .

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

Simplify $2 - (- 2)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} 0 & 4 & 0 - 3 \\ 1 - (- 3) & - 1 - (- 3) & - 1 - 4 \end{array}]$

Simplify $0 - 3$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} 0 & 4 & - 3 \\ 1 - (- 3) & - 1 - (- 3) & - 1 - 4 \end{array}]$

Simplify $1 - (- 3)$ .

$[\begin{array}{c} 0 & 0 & 0 \\ 0 & 0 & 0 \end{array}] - X = [\begin{array}{c} 0 & 4 & - 3 \\ 4 & - 1 - (- 3) & - 1 - 4 \end{array}]$

Simplify $- 1 - (- 3)$ .

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

Simplify $- 1 - 4$ .

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

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

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

Multiply both sides of the equation by $- 1$ .

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

Simplify both sides of the equation.

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Simplify the left side of the equation.

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Multiply $- 1 (- X)$ .

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Multiply $- 1$ by $- 1$ .

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

Multiply $X$ by $1$ .

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

Can’t combine different size matrices.

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

The combined expressions are .

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

Simplify the right side of the equation.

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Multiply $- 1$ by each element of the matrix.

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

Simplify each element of the matrix $[\begin{array}{c} - 1 \cdot 0 & - 1 \cdot 4 & - 1 \cdot - 3 \\ - 1 \cdot 4 & - 1 \cdot 2 & - 1 \cdot - 5 \end{array}]$ .

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Rearrange $- 1 \cdot 0$ .

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

Rearrange $- 1 \cdot 4$ .

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

Rearrange $- 1 \cdot - 3$ .

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

Rearrange $- 1 \cdot 4$ .

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

Rearrange $- 1 \cdot 2$ .

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

Rearrange $- 1 \cdot - 5$ .

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

Solve [[2,-2,3],[-3,-3,4]]-x=[[2,2,0],[1,-1,-1]]

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