Linear Algebra Examples

[\begin{array}{c} 1 & 0 & 1 \\ - 1 & 21 & 0 \end{array}] + [\begin{array}{c} 2 & 2 & - 2 \\ - 3 & 4 & 3 \end{array}]

$[\begin{array}{c} 1 & 0 & 1 \\ - 1 & 21 & 0 \end{array}] + [\begin{array}{c} 2 & 2 & - 2 \\ - 3 & 4 & 3 \end{array}]$

Step 1

Add the corresponding elements.

[\begin{array}{c} 1 + 2 & 0 + 2 & 1 - 2 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]

$[\begin{array}{c} 1 + 2 & 0 + 2 & 1 - 2 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]$

Step 2

Simplify each element.

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Step 2.1

Add

1

$1$ and

2

$2$ .

[\begin{array}{c} 3 & 0 + 2 & 1 - 2 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]

$[\begin{array}{c} 3 & 0 + 2 & 1 - 2 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]$

Step 2.2

Add

0

$0$ and

2

$2$ .

[\begin{array}{c} 3 & 2 & 1 - 2 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]

$[\begin{array}{c} 3 & 2 & 1 - 2 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]$

Step 2.3

Subtract

2

$2$ from

1

$1$ .

[\begin{array}{c} 3 & 2 & - 1 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]

$[\begin{array}{c} 3 & 2 & - 1 \\ - 1 - 3 & 21 + 4 & 0 + 3 \end{array}]$

Step 2.4

Subtract

3

$3$ from

- 1

$- 1$ .

[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 21 + 4 & 0 + 3 \end{array}]

$[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 21 + 4 & 0 + 3 \end{array}]$

Step 2.5

Add

21

$21$ and

4

$4$ .

[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 25 & 0 + 3 \end{array}]

$[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 25 & 0 + 3 \end{array}]$

Step 2.6

Add

0

$0$ and

3

$3$ .

[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 25 & 3 \end{array}]

$[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 25 & 3 \end{array}]$

[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 25 & 3 \end{array}]

$[\begin{array}{c} 3 & 2 & - 1 \\ - 4 & 25 & 3 \end{array}]$

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