Linear Algebra Examples

$[\begin{array}{c} 3 & 6 \end{array}]$

Step 1

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

$\sqrt{3^{2} + 6^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{9 + 6^{2}}$

Step 2.2

Raise $6$ to the power of $2$ .

$\sqrt{9 + 36}$

Step 2.3

Add $9$ and $36$ .

$\sqrt{45}$

Step 2.4

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 2.4.1

Factor $9$ out of $45$ .

$\sqrt{9 (5)}$

Step 2.4.2

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

$\sqrt{3^{2} \cdot 5}$

Step 2.5

Pull terms out from under the radical.

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$3 \sqrt{5}$

Decimal Form:

$6.70820393 \dots$

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