Linear Algebra Examples

$(0.5) [\begin{array}{c} 8 & 18 & 8 & 0 \\ 30 & 24 & 11 & 4 \\ 8 & 29 & 32 & 14 \\ 0 & 29 & 50 & 32 \end{array}]$

Step 1

Multiply $0.5$ by each element of the matrix.

$[\begin{array}{c} 0.5 \cdot 8 & 0.5 \cdot 18 & 0.5 \cdot 8 & 0.5 \cdot 0 \\ 0.5 \cdot 30 & 0.5 \cdot 24 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2

Simplify each element in the matrix.

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Step 2.1

Multiply $0.5$ by $8$ .

$[\begin{array}{c} 4 & 0.5 \cdot 18 & 0.5 \cdot 8 & 0.5 \cdot 0 \\ 0.5 \cdot 30 & 0.5 \cdot 24 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.2

Multiply $0.5$ by $18$ .

$[\begin{array}{c} 4 & 9 & 0.5 \cdot 8 & 0.5 \cdot 0 \\ 0.5 \cdot 30 & 0.5 \cdot 24 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.3

Multiply $0.5$ by $8$ .

$[\begin{array}{c} 4 & 9 & 4 & 0.5 \cdot 0 \\ 0.5 \cdot 30 & 0.5 \cdot 24 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.4

Multiply $0.5$ by $0$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 0.5 \cdot 30 & 0.5 \cdot 24 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.5

Multiply $0.5$ by $30$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 0.5 \cdot 24 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.6

Multiply $0.5$ by $24$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 0.5 \cdot 11 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.7

Multiply $0.5$ by $11$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 0.5 \cdot 4 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.8

Multiply $0.5$ by $4$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 0.5 \cdot 8 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.9

Multiply $0.5$ by $8$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 0.5 \cdot 29 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.10

Multiply $0.5$ by $29$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 0.5 \cdot 32 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.11

Multiply $0.5$ by $32$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 16 & 0.5 \cdot 14 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.12

Multiply $0.5$ by $14$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 16 & 7 \\ 0.5 \cdot 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.13

Multiply $0.5$ by $0$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 16 & 7 \\ 0 & 0.5 \cdot 29 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.14

Multiply $0.5$ by $29$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 16 & 7 \\ 0 & 14.5 & 0.5 \cdot 50 & 0.5 \cdot 32 \end{array}]$

Step 2.15

Multiply $0.5$ by $50$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 16 & 7 \\ 0 & 14.5 & 25 & 0.5 \cdot 32 \end{array}]$

Step 2.16

Multiply $0.5$ by $32$ .

$[\begin{array}{c} 4 & 9 & 4 & 0 \\ 15 & 12 & 5.5 & 2 \\ 4 & 14.5 & 16 & 7 \\ 0 & 14.5 & 25 & 16 \end{array}]$