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

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

Step 1

Multiply $- 2$ by each element of the matrix.

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

Step 2

Simplify each element in the matrix.

Rearrange $- 2 \cdot 4$ .

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

Rearrange $- 2 \cdot 3$ .

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

Rearrange $- 2 \cdot - 1$ .

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

Rearrange $- 2 \cdot 6$ .

$[\begin{array}{c} 5 & 2 \\ 3 & 0 \end{array}] + [\begin{array}{c} - 8 & - 6 \\ 2 & - 12 \end{array}] + [\begin{array}{c} 2 & 8 \\ 0 & 5 \end{array}]$

Step 3

Add the corresponding elements.

$[\begin{array}{c} 5 - 8 & 2 - 6 \\ 3 + 2 & 0 - 12 \end{array}] + [\begin{array}{c} 2 & 8 \\ 0 & 5 \end{array}]$

Step 4

Simplify each element of the matrix $[\begin{array}{c} 5 - 8 & 2 - 6 \\ 3 + 2 & 0 - 12 \end{array}]$ .

Simplify $5 - 8$ .

$[\begin{array}{c} - 3 & 2 - 6 \\ 3 + 2 & 0 - 12 \end{array}] + [\begin{array}{c} 2 & 8 \\ 0 & 5 \end{array}]$

Simplify $2 - 6$ .

$[\begin{array}{c} - 3 & - 4 \\ 3 + 2 & 0 - 12 \end{array}] + [\begin{array}{c} 2 & 8 \\ 0 & 5 \end{array}]$

Simplify $3 + 2$ .

$[\begin{array}{c} - 3 & - 4 \\ 5 & 0 - 12 \end{array}] + [\begin{array}{c} 2 & 8 \\ 0 & 5 \end{array}]$

Simplify $0 - 12$ .

$[\begin{array}{c} - 3 & - 4 \\ 5 & - 12 \end{array}] + [\begin{array}{c} 2 & 8 \\ 0 & 5 \end{array}]$

Step 5

Add the corresponding elements.

$[\begin{array}{c} - 3 + 2 & - 4 + 8 \\ 5 + 0 & - 12 + 5 \end{array}]$

Step 6

Simplify each element of the matrix $[\begin{array}{c} - 3 + 2 & - 4 + 8 \\ 5 + 0 & - 12 + 5 \end{array}]$ .

Simplify $- 3 + 2$ .

$[\begin{array}{c} - 1 & - 4 + 8 \\ 5 + 0 & - 12 + 5 \end{array}]$

Simplify $- 4 + 8$ .

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

Simplify $5 + 0$ .

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

Simplify $- 12 + 5$ .

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

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

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