Simplify the Matrix 6[[-3,0],[5,-7]]+[[-4,2],[-1,8]]

$6 [\begin{array}{c} - 3 & 0 \\ 5 & - 7 \end{array}] + [\begin{array}{c} - 4 & 2 \\ - 1 & 8 \end{array}]$

Step 1

Multiply $6$ by each element of the matrix.

$[\begin{array}{c} 6 \cdot - 3 & 6 \cdot 0 \\ 6 \cdot 5 & 6 \cdot - 7 \end{array}] + [\begin{array}{c} - 4 & 2 \\ - 1 & 8 \end{array}]$

Step 2

Simplify each element in the matrix.

Rearrange $6 \cdot - 3$ .

$[\begin{array}{c} - 18 & 6 \cdot 0 \\ 6 \cdot 5 & 6 \cdot - 7 \end{array}] + [\begin{array}{c} - 4 & 2 \\ - 1 & 8 \end{array}]$

Rearrange $6 \cdot 0$ .

$[\begin{array}{c} - 18 & 0 \\ 6 \cdot 5 & 6 \cdot - 7 \end{array}] + [\begin{array}{c} - 4 & 2 \\ - 1 & 8 \end{array}]$

Rearrange $6 \cdot 5$ .

$[\begin{array}{c} - 18 & 0 \\ 30 & 6 \cdot - 7 \end{array}] + [\begin{array}{c} - 4 & 2 \\ - 1 & 8 \end{array}]$

Rearrange $6 \cdot - 7$ .

$[\begin{array}{c} - 18 & 0 \\ 30 & - 42 \end{array}] + [\begin{array}{c} - 4 & 2 \\ - 1 & 8 \end{array}]$

Step 3

Add the corresponding elements.

$[\begin{array}{c} - 18 - 4 & 0 + 2 \\ 30 - 1 & - 42 + 8 \end{array}]$

Step 4

Simplify each element of the matrix $[\begin{array}{c} - 18 - 4 & 0 + 2 \\ 30 - 1 & - 42 + 8 \end{array}]$ .

Simplify $- 18 - 4$ .

$[\begin{array}{c} - 22 & 0 + 2 \\ 30 - 1 & - 42 + 8 \end{array}]$

Simplify $0 + 2$ .

$[\begin{array}{c} - 22 & 2 \\ 30 - 1 & - 42 + 8 \end{array}]$

Simplify $30 - 1$ .

$[\begin{array}{c} - 22 & 2 \\ 29 & - 42 + 8 \end{array}]$

Simplify $- 42 + 8$ .

$[\begin{array}{c} - 22 & 2 \\ 29 & - 34 \end{array}]$