Solve the Matrix Equation [[5,-7],[1,4]]-x=[[9,4],[7,5]]

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

Step 1

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

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

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

Step 2

Simplify the right side.

Subtract the corresponding elements.

$- x = [\begin{array}{c} 9 - 5 & 4 + 7 \\ 7 - 1 & 5 - 4 \end{array}]$

Simplify each element.

Subtract $5$ from $9$ .

$- x = [\begin{array}{c} 4 & 4 + 7 \\ 7 - 1 & 5 - 4 \end{array}]$

Add $4$ and $7$ .

$- x = [\begin{array}{c} 4 & 11 \\ 7 - 1 & 5 - 4 \end{array}]$

Subtract $1$ from $7$ .

$- x = [\begin{array}{c} 4 & 11 \\ 6 & 5 - 4 \end{array}]$

Subtract $4$ from $5$ .

$- x = [\begin{array}{c} 4 & 11 \\ 6 & 1 \end{array}]$

Step 3

Multiply both sides by $- 1$ .

$- - x = - [\begin{array}{c} 4 & 11 \\ 6 & 1 \end{array}]$

Step 4

Simplify.

Multiply $- - x$ .

Multiply $- 1$ by $- 1$ .

$1 x = - [\begin{array}{c} 4 & 11 \\ 6 & 1 \end{array}]$

Multiply $x$ by $1$ .

$x = - [\begin{array}{c} 4 & 11 \\ 6 & 1 \end{array}]$

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

$x = [\begin{array}{c} - 1 \cdot 4 & - 1 \cdot 11 \\ - 1 \cdot 6 & - 1 \cdot 1 \end{array}]$

Simplify each element in the matrix.

Multiply $- 1$ by $4$ .

$x = [\begin{array}{c} - 4 & - 1 \cdot 11 \\ - 1 \cdot 6 & - 1 \cdot 1 \end{array}]$

Multiply $- 1$ by $11$ .

$x = [\begin{array}{c} - 4 & - 11 \\ - 1 \cdot 6 & - 1 \cdot 1 \end{array}]$

Multiply $- 1$ by $6$ .

$x = [\begin{array}{c} - 4 & - 11 \\ - 6 & - 1 \cdot 1 \end{array}]$

Multiply $- 1$ by $1$ .

$x = [\begin{array}{c} - 4 & - 11 \\ - 6 & - 1 \end{array}]$