Linear Algebra Examples

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

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

Step 1

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

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

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

Step 2

Simplify.

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Step 2.1

Raise

3

$3$ to the power of

2

$2$ .

\sqrt{9 + 6^{2}}

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

Step 2.2

Raise

6

$6$ to the power of

2

$2$ .

\sqrt{9 + 36}

$\sqrt{9 + 36}$

Step 2.3

Add

9

$9$ and

36

$36$ .

\sqrt{45}

$\sqrt{45}$

Step 2.4

Rewrite

45

$45$ as

3^{2} \cdot 5

$3^{2} \cdot 5$ .

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Step 2.4.1

Factor

9

$9$ out of

45

$45$ .

\sqrt{9 (5)}

$\sqrt{9 (5)}$

Step 2.4.2

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

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

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

Step 2.5

Pull terms out from under the radical.

3 \sqrt{5}

$3 \sqrt{5}$

3 \sqrt{5}

$3 \sqrt{5}$

Step 3

The result can be shown in multiple forms.

Exact Form:

3 \sqrt{5}

$3 \sqrt{5}$

Decimal Form:

6.70820393 \dots

$6.70820393 \dots$

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