Linear Algebra Examples

$[\begin{array}{c} 2 \\ 4 \\ 3 \end{array}]$

Step 1

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

$\sqrt{2^{2} + 4^{2} + 3^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{4 + 4^{2} + 3^{2}}$

Step 2.2

Raise $4$ to the power of $2$ .

$\sqrt{4 + 16 + 3^{2}}$

Step 2.3

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

$\sqrt{4 + 16 + 9}$

Step 2.4

Add $4$ and $16$ .

$\sqrt{20 + 9}$

Step 2.5

Add $20$ and $9$ .

$\sqrt{29}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{29}$

Decimal Form:

$5.38516480 \dots$

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