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

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

Step 1

Simplify each term.

Multiply $3$ by each element of the matrix.

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

Simplify each element in the matrix.

Multiply $3$ by $3$ .

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

Multiply $3$ by $5$ .

$[\begin{array}{c} 9 & 15 & 3 \cdot 2 \\ 3 \cdot - 1 & 3 \cdot 8 & 3 \cdot 5 \end{array}] - [\begin{array}{c} 7 & 3 & - 2 \\ 5 & 4 & 3 \end{array}]$

Multiply $3$ by $2$ .

$[\begin{array}{c} 9 & 15 & 6 \\ 3 \cdot - 1 & 3 \cdot 8 & 3 \cdot 5 \end{array}] - [\begin{array}{c} 7 & 3 & - 2 \\ 5 & 4 & 3 \end{array}]$

Multiply $3$ by $- 1$ .

$[\begin{array}{c} 9 & 15 & 6 \\ - 3 & 3 \cdot 8 & 3 \cdot 5 \end{array}] - [\begin{array}{c} 7 & 3 & - 2 \\ 5 & 4 & 3 \end{array}]$

Multiply $3$ by $8$ .

$[\begin{array}{c} 9 & 15 & 6 \\ - 3 & 24 & 3 \cdot 5 \end{array}] - [\begin{array}{c} 7 & 3 & - 2 \\ 5 & 4 & 3 \end{array}]$

Multiply $3$ by $5$ .

$[\begin{array}{c} 9 & 15 & 6 \\ - 3 & 24 & 15 \end{array}] - [\begin{array}{c} 7 & 3 & - 2 \\ 5 & 4 & 3 \end{array}]$

Step 2

Subtract the corresponding elements.

$[\begin{array}{c} 9 - 7 & 15 - 3 & 6 + 2 \\ - 3 - 5 & 24 - 4 & 15 - 3 \end{array}]$

Step 3

Simplify each element.

Subtract $7$ from $9$ .

$[\begin{array}{c} 2 & 15 - 3 & 6 + 2 \\ - 3 - 5 & 24 - 4 & 15 - 3 \end{array}]$

Subtract $3$ from $15$ .

$[\begin{array}{c} 2 & 12 & 6 + 2 \\ - 3 - 5 & 24 - 4 & 15 - 3 \end{array}]$

Add $6$ and $2$ .

$[\begin{array}{c} 2 & 12 & 8 \\ - 3 - 5 & 24 - 4 & 15 - 3 \end{array}]$

Subtract $5$ from $- 3$ .

$[\begin{array}{c} 2 & 12 & 8 \\ - 8 & 24 - 4 & 15 - 3 \end{array}]$

Subtract $4$ from $24$ .

$[\begin{array}{c} 2 & 12 & 8 \\ - 8 & 20 & 15 - 3 \end{array}]$

Subtract $3$ from $15$ .

$[\begin{array}{c} 2 & 12 & 8 \\ - 8 & 20 & 12 \end{array}]$

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

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