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

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

Step 1

Multiply $- 6$ by each element of the matrix.

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

Step 2

Simplify each element in the matrix.

Rearrange $- 6 \cdot - 3$ .

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

Rearrange $- 6 \cdot - 2$ .

$[\begin{array}{c} 4 & 7 \\ - 5 & 1 \end{array}] + [\begin{array}{c} 18 & 12 \\ - 6 \cdot 0 & - 6 \cdot 6 \end{array}]$

Rearrange $- 6 \cdot 0$ .

$[\begin{array}{c} 4 & 7 \\ - 5 & 1 \end{array}] + [\begin{array}{c} 18 & 12 \\ 0 & - 6 \cdot 6 \end{array}]$

Rearrange $- 6 \cdot 6$ .

$[\begin{array}{c} 4 & 7 \\ - 5 & 1 \end{array}] + [\begin{array}{c} 18 & 12 \\ 0 & - 36 \end{array}]$

Step 3

Add the corresponding elements.

$[\begin{array}{c} 4 + 18 & 7 + 12 \\ - 5 + 0 & 1 - 36 \end{array}]$

Step 4

Simplify each element of the matrix $[\begin{array}{c} 4 + 18 & 7 + 12 \\ - 5 + 0 & 1 - 36 \end{array}]$ .

Simplify $4 + 18$ .

$[\begin{array}{c} 22 & 7 + 12 \\ - 5 + 0 & 1 - 36 \end{array}]$

Simplify $7 + 12$ .

$[\begin{array}{c} 22 & 19 \\ - 5 + 0 & 1 - 36 \end{array}]$

Simplify $- 5 + 0$ .

$[\begin{array}{c} 22 & 19 \\ - 5 & 1 - 36 \end{array}]$

Simplify $1 - 36$ .

$[\begin{array}{c} 22 & 19 \\ - 5 & - 35 \end{array}]$