Linear Algebra Examples

$[\begin{array}{c} 4 & 5 & 0 \\ 11 & 1 & 2 \\ 1 & 5 & 2 \end{array}]$

Step 1

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

$\sqrt{4^{2} + 5^{2} + 0^{2} + 11^{2} + 1^{2} + 2^{2} + 1^{2} + 5^{2} + 2^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{16 + 5^{2} + 0^{2} + 11^{2} + 1^{2} + 2^{2} + 1^{2} + 5^{2} + 2^{2}}$

Step 2.2

Raise $5$ to the power of $2$ .

$\sqrt{16 + 25 + 0^{2} + 11^{2} + 1^{2} + 2^{2} + 1^{2} + 5^{2} + 2^{2}}$

Step 2.3

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

$\sqrt{16 + 25 + 0 + 11^{2} + 1^{2} + 2^{2} + 1^{2} + 5^{2} + 2^{2}}$

Step 2.4

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

$\sqrt{16 + 25 + 0 + 121 + 1^{2} + 2^{2} + 1^{2} + 5^{2} + 2^{2}}$

Step 2.5

One to any power is one.

$\sqrt{16 + 25 + 0 + 121 + 1 + 2^{2} + 1^{2} + 5^{2} + 2^{2}}$

Step 2.6

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

$\sqrt{16 + 25 + 0 + 121 + 1 + 4 + 1^{2} + 5^{2} + 2^{2}}$

Step 2.7

One to any power is one.

$\sqrt{16 + 25 + 0 + 121 + 1 + 4 + 1 + 5^{2} + 2^{2}}$

Step 2.8

Raise $5$ to the power of $2$ .

$\sqrt{16 + 25 + 0 + 121 + 1 + 4 + 1 + 25 + 2^{2}}$

Step 2.9

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

$\sqrt{16 + 25 + 0 + 121 + 1 + 4 + 1 + 25 + 4}$

Step 2.10

Add $16$ and $25$ .

$\sqrt{41 + 0 + 121 + 1 + 4 + 1 + 25 + 4}$

Step 2.11

Add $41$ and $0$ .

$\sqrt{41 + 121 + 1 + 4 + 1 + 25 + 4}$

Step 2.12

Add $41$ and $121$ .

$\sqrt{162 + 1 + 4 + 1 + 25 + 4}$

Step 2.13

Add $162$ and $1$ .

$\sqrt{163 + 4 + 1 + 25 + 4}$

Step 2.14

Add $163$ and $4$ .

$\sqrt{167 + 1 + 25 + 4}$

Step 2.15

Add $167$ and $1$ .

$\sqrt{168 + 25 + 4}$

Step 2.16

Add $168$ and $25$ .

$\sqrt{193 + 4}$

Step 2.17

Add $193$ and $4$ .

$\sqrt{197}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{197}$

Decimal Form:

$14.03566884 \dots$