Finite Math Examples

$2 [\begin{array}{c} 5 & - 2 \\ 10 & - 4 \end{array}] - 3 [\begin{array}{c} 2 & - 7 \\ - 3 & 5 \\ 4 & - 6 \end{array}]$

Step 1

Multiply $2$ by each element of the matrix.

$[\begin{array}{c} 2 \cdot 5 & 2 \cdot - 2 \\ 2 \cdot 10 & 2 \cdot - 4 \end{array}] - 3 [\begin{array}{c} 2 & - 7 \\ - 3 & 5 \\ 4 & - 6 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $2$ by $5$ .

$[\begin{array}{c} 10 & 2 \cdot - 2 \\ 2 \cdot 10 & 2 \cdot - 4 \end{array}] - 3 [\begin{array}{c} 2 & - 7 \\ - 3 & 5 \\ 4 & - 6 \end{array}]$

Step 2.2

Multiply $2$ by $- 2$ .

$[\begin{array}{c} 10 & - 4 \\ 2 \cdot 10 & 2 \cdot - 4 \end{array}] - 3 [\begin{array}{c} 2 & - 7 \\ - 3 & 5 \\ 4 & - 6 \end{array}]$

Step 2.3

Multiply $2$ by $10$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & 2 \cdot - 4 \end{array}] - 3 [\begin{array}{c} 2 & - 7 \\ - 3 & 5 \\ 4 & - 6 \end{array}]$

Step 2.4

Multiply $2$ by $- 4$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] - 3 [\begin{array}{c} 2 & - 7 \\ - 3 & 5 \\ 4 & - 6 \end{array}]$

Step 3

Multiply $- 3$ by each element of the matrix.

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 3 \cdot 2 & - 3 \cdot - 7 \\ - 3 \cdot - 3 & - 3 \cdot 5 \\ - 3 \cdot 4 & - 3 \cdot - 6 \end{array}]$

Step 4

Simplify each element in the matrix.

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Step 4.1

Multiply $- 3$ by $2$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 6 & - 3 \cdot - 7 \\ - 3 \cdot - 3 & - 3 \cdot 5 \\ - 3 \cdot 4 & - 3 \cdot - 6 \end{array}]$

Step 4.2

Multiply $- 3$ by $- 7$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 6 & 21 \\ - 3 \cdot - 3 & - 3 \cdot 5 \\ - 3 \cdot 4 & - 3 \cdot - 6 \end{array}]$

Step 4.3

Multiply $- 3$ by $- 3$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 6 & 21 \\ 9 & - 3 \cdot 5 \\ - 3 \cdot 4 & - 3 \cdot - 6 \end{array}]$

Step 4.4

Multiply $- 3$ by $5$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 6 & 21 \\ 9 & - 15 \\ - 3 \cdot 4 & - 3 \cdot - 6 \end{array}]$

Step 4.5

Multiply $- 3$ by $4$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 6 & 21 \\ 9 & - 15 \\ - 12 & - 3 \cdot - 6 \end{array}]$

Step 4.6

Multiply $- 3$ by $- 6$ .

$[\begin{array}{c} 10 & - 4 \\ 20 & - 8 \end{array}] + [\begin{array}{c} - 6 & 21 \\ 9 & - 15 \\ - 12 & 18 \end{array}]$