Linear Algebra Examples

$[\begin{array}{c} 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 3 & 8 & 15 & 24 & 35 & 48 \end{array}] \cdot 6$

Step 1

Move $6$ to the left of $[\begin{array}{c} 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 3 & 8 & 15 & 24 & 35 & 48 \end{array}]$ .

$6 \cdot [\begin{array}{c} 1 & 2 & 3 & 4 & 5 & 6 & 7 \\ 0 & 3 & 8 & 15 & 24 & 35 & 48 \end{array}]$

Step 2

Multiply $6$ by each element of the matrix.

$[\begin{array}{c} 6 \cdot 1 & 6 \cdot 2 & 6 \cdot 3 & 6 \cdot 4 & 6 \cdot 5 & 6 \cdot 6 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3

Simplify each element in the matrix.

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Step 3.1

Multiply $6$ by $1$ .

$[\begin{array}{c} 6 & 6 \cdot 2 & 6 \cdot 3 & 6 \cdot 4 & 6 \cdot 5 & 6 \cdot 6 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.2

Multiply $6$ by $2$ .

$[\begin{array}{c} 6 & 12 & 6 \cdot 3 & 6 \cdot 4 & 6 \cdot 5 & 6 \cdot 6 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.3

Multiply $6$ by $3$ .

$[\begin{array}{c} 6 & 12 & 18 & 6 \cdot 4 & 6 \cdot 5 & 6 \cdot 6 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.4

Multiply $6$ by $4$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 6 \cdot 5 & 6 \cdot 6 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.5

Multiply $6$ by $5$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 6 \cdot 6 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.6

Multiply $6$ by $6$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 6 \cdot 7 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.7

Multiply $6$ by $7$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 6 \cdot 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.8

Multiply $6$ by $0$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 6 \cdot 3 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.9

Multiply $6$ by $3$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 18 & 6 \cdot 8 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.10

Multiply $6$ by $8$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 18 & 48 & 6 \cdot 15 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.11

Multiply $6$ by $15$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 18 & 48 & 90 & 6 \cdot 24 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.12

Multiply $6$ by $24$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 18 & 48 & 90 & 144 & 6 \cdot 35 & 6 \cdot 48 \end{array}]$

Step 3.13

Multiply $6$ by $35$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 18 & 48 & 90 & 144 & 210 & 6 \cdot 48 \end{array}]$

Step 3.14

Multiply $6$ by $48$ .

$[\begin{array}{c} 6 & 12 & 18 & 24 & 30 & 36 & 42 \\ 0 & 18 & 48 & 90 & 144 & 210 & 288 \end{array}]$