Linear Algebra Examples

[\begin{array}{c} 1 \\ 4 \\ 4 \end{array}]

$[\begin{array}{c} 1 \\ 4 \\ 4 \end{array}]$

Step 1

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

\sqrt{1^{2} + 4^{2} + 4^{2}}

$\sqrt{1^{2} + 4^{2} + 4^{2}}$

Step 2

Simplify.

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Step 2.1

One to any power is one.

\sqrt{1 + 4^{2} + 4^{2}}

$\sqrt{1 + 4^{2} + 4^{2}}$

Step 2.2

Raise

4

$4$ to the power of

2

$2$ .

\sqrt{1 + 16 + 4^{2}}

$\sqrt{1 + 16 + 4^{2}}$

Step 2.3

Raise

4

$4$ to the power of

2

$2$ .

\sqrt{1 + 16 + 16}

$\sqrt{1 + 16 + 16}$

Step 2.4

Add

1

$1$ and

16

$16$ .

\sqrt{17 + 16}

$\sqrt{17 + 16}$

Step 2.5

Add

17

$17$ and

16

$16$ .

\sqrt{33}

$\sqrt{33}$

\sqrt{33}

$\sqrt{33}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\sqrt{33}

$\sqrt{33}$

Decimal Form:

5.74456264 \dots

$5.74456264 \dots$

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