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

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

Step 1

Move all terms not containing a variable to the right side.

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

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

Step 2

Simplify the right side.

Subtract the corresponding elements.

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

Simplify each element.

Subtract $2$ from $2$ .

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

Add $2$ and $2$ .

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

Subtract $3$ from $0$ .

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

Add $1$ and $3$ .

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

Add $- 1$ and $3$ .

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

Subtract $4$ from $- 1$ .

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

Step 3

Multiply both sides by $- 1$ .

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

Step 4

Simplify.

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

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

Multiply $x$ by $1$ .

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

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

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

Simplify each element in the matrix.

Multiply $- 1$ by $0$ .

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

Multiply $- 1$ by $4$ .

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

Multiply $- 1$ by $- 3$ .

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

Multiply $- 1$ by $4$ .

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

Multiply $- 1$ by $2$ .

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

Multiply $- 1$ by $- 5$ .

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

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

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