Linear Algebra Examples

$[\begin{array}{c} 8 \\ - 16 \\ 11 \end{array}]$

Step 1

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

$\sqrt{8^{2} + {(- 16)}^{2} + 11^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $8$ to the power of $2$ .

$\sqrt{64 + {(- 16)}^{2} + 11^{2}}$

Step 2.2

Raise $- 16$ to the power of $2$ .

$\sqrt{64 + 256 + 11^{2}}$

Step 2.3

Raise $11$ to the power of $2$ .

$\sqrt{64 + 256 + 121}$

Step 2.4

Add $64$ and $256$ .

$\sqrt{320 + 121}$

Step 2.5

Add $320$ and $121$ .

$\sqrt{441}$

Step 2.6

Rewrite $441$ as $21^{2}$ .

$\sqrt{21^{2}}$

Step 2.7

Pull terms out from under the radical, assuming positive real numbers.

$21$