Linear Algebra Examples

$[\begin{array}{c} 0 \\ 3 \\ 4 \end{array}]$

Step 1

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

$\sqrt{0^{2} + 3^{2} + 4^{2}}$

Step 2

Simplify.

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Step 2.1

Raising $0$ to any positive power yields $0$ .

$\sqrt{0 + 3^{2} + 4^{2}}$

Step 2.2

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

$\sqrt{0 + 9 + 4^{2}}$

Step 2.3

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

$\sqrt{0 + 9 + 16}$

Step 2.4

Add $0$ and $9$ .

$\sqrt{9 + 16}$

Step 2.5

Add $9$ and $16$ .

$\sqrt{25}$

Step 2.6

Rewrite $25$ as $5^{2}$ .

$\sqrt{5^{2}}$

Step 2.7

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

$5$

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