Linear Algebra Examples

$[\begin{array}{c} 3 & 4 & 24 \\ 7 & 1 & 31 \end{array}]$

Step 1

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

$\sqrt{3^{2} + 4^{2} + 24^{2} + 7^{2} + 1^{2} + 31^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{9 + 4^{2} + 24^{2} + 7^{2} + 1^{2} + 31^{2}}$

Step 2.2

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

$\sqrt{9 + 16 + 24^{2} + 7^{2} + 1^{2} + 31^{2}}$

Step 2.3

Raise $24$ to the power of $2$ .

$\sqrt{9 + 16 + 576 + 7^{2} + 1^{2} + 31^{2}}$

Step 2.4

Raise $7$ to the power of $2$ .

$\sqrt{9 + 16 + 576 + 49 + 1^{2} + 31^{2}}$

Step 2.5

One to any power is one.

$\sqrt{9 + 16 + 576 + 49 + 1 + 31^{2}}$

Step 2.6

Raise $31$ to the power of $2$ .

$\sqrt{9 + 16 + 576 + 49 + 1 + 961}$

Step 2.7

Add $9$ and $16$ .

$\sqrt{25 + 576 + 49 + 1 + 961}$

Step 2.8

Add $25$ and $576$ .

$\sqrt{601 + 49 + 1 + 961}$

Step 2.9

Add $601$ and $49$ .

$\sqrt{650 + 1 + 961}$

Step 2.10

Add $650$ and $1$ .

$\sqrt{651 + 961}$

Step 2.11

Add $651$ and $961$ .

$\sqrt{1612}$

Step 2.12

Rewrite $1612$ as $2^{2} \cdot 403$ .

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Step 2.12.1

Factor $4$ out of $1612$ .

$\sqrt{4 (403)}$

Step 2.12.2

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 403}$

Step 2.13

Pull terms out from under the radical.

$2 \sqrt{403}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{403}$

Decimal Form:

$40.14971979 \dots$