Linear Algebra Examples

$(3) [\begin{array}{c} 4 & 5 & 6 & 7 \\ 1 & 2 & 4 & 4 \\ 5 & 6 & 7 & 7 \end{array}]$

Step 1

Multiply $3$ by each element of the matrix.

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

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $3$ by $4$ .

$[\begin{array}{c} 12 & 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 \\ 3 \cdot 1 & 3 \cdot 2 & 3 \cdot 4 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.2

Multiply $3$ by $5$ .

$[\begin{array}{c} 12 & 15 & 3 \cdot 6 & 3 \cdot 7 \\ 3 \cdot 1 & 3 \cdot 2 & 3 \cdot 4 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.3

Multiply $3$ by $6$ .

$[\begin{array}{c} 12 & 15 & 18 & 3 \cdot 7 \\ 3 \cdot 1 & 3 \cdot 2 & 3 \cdot 4 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.4

Multiply $3$ by $7$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 \cdot 1 & 3 \cdot 2 & 3 \cdot 4 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.5

Multiply $3$ by $1$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 3 \cdot 2 & 3 \cdot 4 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.6

Multiply $3$ by $2$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 3 \cdot 4 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.7

Multiply $3$ by $4$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 12 & 3 \cdot 4 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.8

Multiply $3$ by $4$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 12 & 12 \\ 3 \cdot 5 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.9

Multiply $3$ by $5$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 12 & 12 \\ 15 & 3 \cdot 6 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.10

Multiply $3$ by $6$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 12 & 12 \\ 15 & 18 & 3 \cdot 7 & 3 \cdot 7 \end{array}]$

Step 2.11

Multiply $3$ by $7$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 12 & 12 \\ 15 & 18 & 21 & 3 \cdot 7 \end{array}]$

Step 2.12

Multiply $3$ by $7$ .

$[\begin{array}{c} 12 & 15 & 18 & 21 \\ 3 & 6 & 12 & 12 \\ 15 & 18 & 21 & 21 \end{array}]$