Solve the Matrix Equation [[3,4,7],[2,5,1],[8,2,5]]-x=[[2,6,8],[3,9,3],[2,5,1]]

$[\begin{array}{c} 3 & 4 & 7 \\ 2 & 5 & 1 \\ 8 & 2 & 5 \end{array}] - x = [\begin{array}{c} 2 & 6 & 8 \\ 3 & 9 & 3 \\ 2 & 5 & 1 \end{array}]$

Step 1

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

Subtract $[\begin{array}{c} 3 & 4 & 7 \\ 2 & 5 & 1 \\ 8 & 2 & 5 \end{array}]$ from both sides of the equation.

$- x = [\begin{array}{c} 2 & 6 & 8 \\ 3 & 9 & 3 \\ 2 & 5 & 1 \end{array}] - [\begin{array}{c} 3 & 4 & 7 \\ 2 & 5 & 1 \\ 8 & 2 & 5 \end{array}]$

Step 2

Simplify the right side.

Subtract the corresponding elements.

$- x = [\begin{array}{c} 2 - 3 & 6 - 4 & 8 - 7 \\ 3 - 2 & 9 - 5 & 3 - 1 \\ 2 - 8 & 5 - 2 & 1 - 5 \end{array}]$

Simplify each element.

Subtract $3$ from $2$ .

$- x = [\begin{array}{c} - 1 & 6 - 4 & 8 - 7 \\ 3 - 2 & 9 - 5 & 3 - 1 \\ 2 - 8 & 5 - 2 & 1 - 5 \end{array}]$

Subtract $4$ from $6$ .

$- x = [\begin{array}{c} - 1 & 2 & 8 - 7 \\ 3 - 2 & 9 - 5 & 3 - 1 \\ 2 - 8 & 5 - 2 & 1 - 5 \end{array}]$

Subtract $7$ from $8$ .

$- x = [\begin{array}{c} - 1 & 2 & 1 \\ 3 - 2 & 9 - 5 & 3 - 1 \\ 2 - 8 & 5 - 2 & 1 - 5 \end{array}]$

Subtract $2$ from $3$ .

$- x = [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 9 - 5 & 3 - 1 \\ 2 - 8 & 5 - 2 & 1 - 5 \end{array}]$

Subtract $5$ from $9$ .

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

Subtract $1$ from $3$ .

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

Subtract $8$ from $2$ .

$- x = [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 4 & 2 \\ - 6 & 5 - 2 & 1 - 5 \end{array}]$

Subtract $2$ from $5$ .

$- x = [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 4 & 2 \\ - 6 & 3 & 1 - 5 \end{array}]$

Subtract $5$ from $1$ .

$- x = [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 4 & 2 \\ - 6 & 3 & - 4 \end{array}]$

Step 3

Multiply both sides by $- 1$ .

$- - x = - [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 4 & 2 \\ - 6 & 3 & - 4 \end{array}]$

Step 4

Simplify.

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x = - [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 4 & 2 \\ - 6 & 3 & - 4 \end{array}]$

Multiply $x$ by $1$ .

$x = - [\begin{array}{c} - 1 & 2 & 1 \\ 1 & 4 & 2 \\ - 6 & 3 & - 4 \end{array}]$

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

$x = [\begin{array}{c} - - 1 & - 1 \cdot 2 & - 1 \cdot 1 \\ - 1 \cdot 1 & - 1 \cdot 4 & - 1 \cdot 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Simplify each element in the matrix.

Multiply $- 1$ by $- 1$ .

$x = [\begin{array}{c} 1 & - 1 \cdot 2 & - 1 \cdot 1 \\ - 1 \cdot 1 & - 1 \cdot 4 & - 1 \cdot 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $2$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \cdot 1 \\ - 1 \cdot 1 & - 1 \cdot 4 & - 1 \cdot 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $1$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 \cdot 1 & - 1 \cdot 4 & - 1 \cdot 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $1$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 & - 1 \cdot 4 & - 1 \cdot 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $4$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 & - 4 & - 1 \cdot 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $2$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 & - 4 & - 2 \\ - - 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $- 6$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 & - 4 & - 2 \\ 6 & - 1 \cdot 3 & - - 4 \end{array}]$

Multiply $- 1$ by $3$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 & - 4 & - 2 \\ 6 & - 3 & - - 4 \end{array}]$

Multiply $- 1$ by $- 4$ .

$x = [\begin{array}{c} 1 & - 2 & - 1 \\ - 1 & - 4 & - 2 \\ 6 & - 3 & 4 \end{array}]$

Solve the Matrix Equation [[3,4,7],[2,5,1],[8,2,5]]-x=[[2,6,8],[3,9,3],[2,5,1]]

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