Linear Algebra Examples

$[\begin{array}{c} 4 & - 2 & 3 \\ - 4 & 4 & - 6 \\ - 4 & 1 & 1 \end{array}] - [\begin{array}{c} 5 & 0 & 0 \\ 0 & 5 & 0 \\ 0 & 0 & 5 \end{array}]$

Step 1

Subtract the corresponding elements.

$[\begin{array}{c} 4 - 5 & - 2 - 0 & 3 - 0 \\ - 4 - 0 & 4 - 5 & - 6 - 0 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Subtract $5$ from $4$ .

$[\begin{array}{c} - 1 & - 2 - 0 & 3 - 0 \\ - 4 - 0 & 4 - 5 & - 6 - 0 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.2

Subtract $0$ from $- 2$ .

$[\begin{array}{c} - 1 & - 2 & 3 - 0 \\ - 4 - 0 & 4 - 5 & - 6 - 0 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.3

Subtract $0$ from $3$ .

$[\begin{array}{c} - 1 & - 2 & 3 \\ - 4 - 0 & 4 - 5 & - 6 - 0 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.4

Subtract $0$ from $- 4$ .

$[\begin{array}{c} - 1 & - 2 & 3 \\ - 4 & 4 - 5 & - 6 - 0 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.5

Subtract $5$ from $4$ .

$[\begin{array}{c} - 1 & - 2 & 3 \\ - 4 & - 1 & - 6 - 0 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.6

Subtract $0$ from $- 6$ .

$[\begin{array}{c} - 1 & - 2 & 3 \\ - 4 & - 1 & - 6 \\ - 4 - 0 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.7

Subtract $0$ from $- 4$ .

$[\begin{array}{c} - 1 & - 2 & 3 \\ - 4 & - 1 & - 6 \\ - 4 & 1 - 0 & 1 - 5 \end{array}]$

Step 2.8

Subtract $0$ from $1$ .

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

Step 2.9

Subtract $5$ from $1$ .

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