Linear Algebra Examples

$3 B [\begin{array}{c} 6 & 9 & 0 & 1 \\ 8 & 2 & 9 & 0 \\ 7 & 8 & 3 & 5 \end{array}]$

Step 1

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

$[\begin{array}{c} 3 B \cdot 6 & 3 B \cdot 9 & 3 B \cdot 0 & 3 B \cdot 1 \\ 3 B \cdot 8 & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2

Simplify each element in the matrix.

Tap for more steps...

Step 2.1

Multiply $6$ by $3$ .

$[\begin{array}{c} 18 B & 3 B \cdot 9 & 3 B \cdot 0 & 3 B \cdot 1 \\ 3 B \cdot 8 & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.2

Multiply $9$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 3 B \cdot 0 & 3 B \cdot 1 \\ 3 B \cdot 8 & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.3

Multiply $3 B \cdot 0$ .

Tap for more steps...

Step 2.3.1

Multiply $0$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 B & 3 B \cdot 1 \\ 3 B \cdot 8 & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.3.2

Multiply $0$ by $B$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \cdot 1 \\ 3 B \cdot 8 & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.4

Multiply $3$ by $1$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 3 B \cdot 8 & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.5

Multiply $8$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 3 B \cdot 2 & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.6

Multiply $2$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 3 B \cdot 9 & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.7

Multiply $9$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 3 B \cdot 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.8

Multiply $3 B \cdot 0$ .

Tap for more steps...

Step 2.8.1

Multiply $0$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 0 B \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.8.2

Multiply $0$ by $B$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 0 \\ 3 B \cdot 7 & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.9

Multiply $7$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 0 \\ 21 B & 3 B \cdot 8 & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.10

Multiply $8$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 0 \\ 21 B & 24 B & 3 B \cdot 3 & 3 B \cdot 5 \end{array}]$

Step 2.11

Multiply $3$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 0 \\ 21 B & 24 B & 9 B & 3 B \cdot 5 \end{array}]$

Step 2.12

Multiply $5$ by $3$ .

$[\begin{array}{c} 18 B & 27 B & 0 & 3 B \\ 24 B & 6 B & 27 B & 0 \\ 21 B & 24 B & 9 B & 15 B \end{array}]$