Linear Algebra Examples

$[\begin{array}{c} 3 \\ 0 \\ 3 \end{array}]$

Step 1

The norm is the square root of the sum of squares of each element in the vector.

$\sqrt{3^{2} + 0^{2} + 3^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $3$ to the power of $2$ .

$\sqrt{9 + 0^{2} + 3^{2}}$

Step 2.2

Raising $0$ to any positive power yields $0$ .

$\sqrt{9 + 0 + 3^{2}}$

Step 2.3

Raise $3$ to the power of $2$ .

$\sqrt{9 + 0 + 9}$

Step 2.4

Add $9$ and $0$ .

$\sqrt{9 + 9}$

Step 2.5

Add $9$ and $9$ .

$\sqrt{18}$

Step 2.6

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 2.6.1

Factor $9$ out of $18$ .

$\sqrt{9 (2)}$

Step 2.6.2

Rewrite $9$ as $3^{2}$ .

$\sqrt{3^{2} \cdot 2}$

Step 2.7

Pull terms out from under the radical.

$3 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{2}$

Decimal Form:

$4.24264068 \dots$

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