Finite Math Examples

$3 [\begin{array}{c} 1 & 1 & - 3 \\ 3 & 2 & 3 \\ 7 & - 1 & 6 \end{array}] + 4 [\begin{array}{c} - 2 & - 1 & 8 \\ 4 & 2 & 2 \\ 3 & 6 & 3 \end{array}]$

Step 1

Simplify each term.

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Step 1.1

Multiply $3$ by each element of the matrix.

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

Step 1.2

Simplify each element in the matrix.

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Step 1.2.1

Multiply $3$ by $1$ .

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

Step 1.2.2

Multiply $3$ by $1$ .

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

Step 1.2.3

Multiply $3$ by $- 3$ .

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

Step 1.2.4

Multiply $3$ by $3$ .

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

Step 1.2.5

Multiply $3$ by $2$ .

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

Step 1.2.6

Multiply $3$ by $3$ .

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

Step 1.2.7

Multiply $3$ by $7$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & 3 \cdot - 1 & 3 \cdot 6 \end{array}] + 4 [\begin{array}{c} - 2 & - 1 & 8 \\ 4 & 2 & 2 \\ 3 & 6 & 3 \end{array}]$

Step 1.2.8

Multiply $3$ by $- 1$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 3 \cdot 6 \end{array}] + 4 [\begin{array}{c} - 2 & - 1 & 8 \\ 4 & 2 & 2 \\ 3 & 6 & 3 \end{array}]$

Step 1.2.9

Multiply $3$ by $6$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + 4 [\begin{array}{c} - 2 & - 1 & 8 \\ 4 & 2 & 2 \\ 3 & 6 & 3 \end{array}]$

Step 1.3

Multiply $4$ by each element of the matrix.

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} 4 \cdot - 2 & 4 \cdot - 1 & 4 \cdot 8 \\ 4 \cdot 4 & 4 \cdot 2 & 4 \cdot 2 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4

Simplify each element in the matrix.

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Step 1.4.1

Multiply $4$ by $- 2$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & 4 \cdot - 1 & 4 \cdot 8 \\ 4 \cdot 4 & 4 \cdot 2 & 4 \cdot 2 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.2

Multiply $4$ by $- 1$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 4 \cdot 8 \\ 4 \cdot 4 & 4 \cdot 2 & 4 \cdot 2 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.3

Multiply $4$ by $8$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 4 \cdot 4 & 4 \cdot 2 & 4 \cdot 2 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.4

Multiply $4$ by $4$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 16 & 4 \cdot 2 & 4 \cdot 2 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.5

Multiply $4$ by $2$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 16 & 8 & 4 \cdot 2 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.6

Multiply $4$ by $2$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 16 & 8 & 8 \\ 4 \cdot 3 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.7

Multiply $4$ by $3$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 16 & 8 & 8 \\ 12 & 4 \cdot 6 & 4 \cdot 3 \end{array}]$

Step 1.4.8

Multiply $4$ by $6$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 16 & 8 & 8 \\ 12 & 24 & 4 \cdot 3 \end{array}]$

Step 1.4.9

Multiply $4$ by $3$ .

$[\begin{array}{c} 3 & 3 & - 9 \\ 9 & 6 & 9 \\ 21 & - 3 & 18 \end{array}] + [\begin{array}{c} - 8 & - 4 & 32 \\ 16 & 8 & 8 \\ 12 & 24 & 12 \end{array}]$

Step 2

Add the corresponding elements.

$[\begin{array}{c} 3 - 8 & 3 - 4 & - 9 + 32 \\ 9 + 16 & 6 + 8 & 9 + 8 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3

Simplify each element.

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Step 3.1

Subtract $8$ from $3$ .

$[\begin{array}{c} - 5 & 3 - 4 & - 9 + 32 \\ 9 + 16 & 6 + 8 & 9 + 8 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.2

Subtract $4$ from $3$ .

$[\begin{array}{c} - 5 & - 1 & - 9 + 32 \\ 9 + 16 & 6 + 8 & 9 + 8 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.3

Add $- 9$ and $32$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 9 + 16 & 6 + 8 & 9 + 8 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.4

Add $9$ and $16$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 25 & 6 + 8 & 9 + 8 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.5

Add $6$ and $8$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 25 & 14 & 9 + 8 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.6

Add $9$ and $8$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 25 & 14 & 17 \\ 21 + 12 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.7

Add $21$ and $12$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 25 & 14 & 17 \\ 33 & - 3 + 24 & 18 + 12 \end{array}]$

Step 3.8

Add $- 3$ and $24$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 25 & 14 & 17 \\ 33 & 21 & 18 + 12 \end{array}]$

Step 3.9

Add $18$ and $12$ .

$[\begin{array}{c} - 5 & - 1 & 23 \\ 25 & 14 & 17 \\ 33 & 21 & 30 \end{array}]$