Algebra Examples

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

Step 1

Simplify each term.

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Multiply $2$ by each element of the matrix.

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

Simplify each element in the matrix.

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Multiply $2$ by $3$ .

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

Multiply $2$ by $4$ .

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

Multiply $2$ by $6$ .

$[\begin{array}{c} 6 & 8 \\ 12 & 2 \cdot - 2 \\ 2 \cdot 1 & 2 \cdot 0 \end{array}] - 5 [\begin{array}{c} - 3 & 1 \\ 2 & - 4 \\ - 1 & 5 \end{array}]$

Multiply $2$ by $- 2$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 \cdot 1 & 2 \cdot 0 \end{array}] - 5 [\begin{array}{c} - 3 & 1 \\ 2 & - 4 \\ - 1 & 5 \end{array}]$

Multiply $2$ by $1$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 2 \cdot 0 \end{array}] - 5 [\begin{array}{c} - 3 & 1 \\ 2 & - 4 \\ - 1 & 5 \end{array}]$

Multiply $2$ by $0$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] - 5 [\begin{array}{c} - 3 & 1 \\ 2 & - 4 \\ - 1 & 5 \end{array}]$

Multiply $- 5$ by each element of the matrix.

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} - 5 \cdot - 3 & - 5 \cdot 1 \\ - 5 \cdot 2 & - 5 \cdot - 4 \\ - 5 \cdot - 1 & - 5 \cdot 5 \end{array}]$

Simplify each element in the matrix.

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Multiply $- 5$ by $- 3$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} 15 & - 5 \cdot 1 \\ - 5 \cdot 2 & - 5 \cdot - 4 \\ - 5 \cdot - 1 & - 5 \cdot 5 \end{array}]$

Multiply $- 5$ by $1$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} 15 & - 5 \\ - 5 \cdot 2 & - 5 \cdot - 4 \\ - 5 \cdot - 1 & - 5 \cdot 5 \end{array}]$

Multiply $- 5$ by $2$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} 15 & - 5 \\ - 10 & - 5 \cdot - 4 \\ - 5 \cdot - 1 & - 5 \cdot 5 \end{array}]$

Multiply $- 5$ by $- 4$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} 15 & - 5 \\ - 10 & 20 \\ - 5 \cdot - 1 & - 5 \cdot 5 \end{array}]$

Multiply $- 5$ by $- 1$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} 15 & - 5 \\ - 10 & 20 \\ 5 & - 5 \cdot 5 \end{array}]$

Multiply $- 5$ by $5$ .

$[\begin{array}{c} 6 & 8 \\ 12 & - 4 \\ 2 & 0 \end{array}] + [\begin{array}{c} 15 & - 5 \\ - 10 & 20 \\ 5 & - 25 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} 6 + 15 & 8 - 5 \\ 12 - 10 & - 4 + 20 \\ 2 + 5 & 0 - 25 \end{array}]$

Step 3

Simplify each element.

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Add $6$ and $15$ .

$[\begin{array}{c} 21 & 8 - 5 \\ 12 - 10 & - 4 + 20 \\ 2 + 5 & 0 - 25 \end{array}]$

Subtract $5$ from $8$ .

$[\begin{array}{c} 21 & 3 \\ 12 - 10 & - 4 + 20 \\ 2 + 5 & 0 - 25 \end{array}]$

Subtract $10$ from $12$ .

$[\begin{array}{c} 21 & 3 \\ 2 & - 4 + 20 \\ 2 + 5 & 0 - 25 \end{array}]$

Add $- 4$ and $20$ .

$[\begin{array}{c} 21 & 3 \\ 2 & 16 \\ 2 + 5 & 0 - 25 \end{array}]$

Add $2$ and $5$ .

$[\begin{array}{c} 21 & 3 \\ 2 & 16 \\ 7 & 0 - 25 \end{array}]$

Subtract $25$ from $0$ .

$[\begin{array}{c} 21 & 3 \\ 2 & 16 \\ 7 & - 25 \end{array}]$