Linear Algebra Examples

$[\begin{array}{c} 1 & 2 & 1 \\ 1 & 2 & 1 \end{array}]$

Step 1

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

$\sqrt{1^{2} + 2^{2} + 1^{2} + 1^{2} + 2^{2} + 1^{2}}$

Step 2

Simplify.

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Step 2.1

One to any power is one.

$\sqrt{1 + 2^{2} + 1^{2} + 1^{2} + 2^{2} + 1^{2}}$

Step 2.2

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

$\sqrt{1 + 4 + 1^{2} + 1^{2} + 2^{2} + 1^{2}}$

Step 2.3

One to any power is one.

$\sqrt{1 + 4 + 1 + 1^{2} + 2^{2} + 1^{2}}$

Step 2.4

One to any power is one.

$\sqrt{1 + 4 + 1 + 1 + 2^{2} + 1^{2}}$

Step 2.5

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

$\sqrt{1 + 4 + 1 + 1 + 4 + 1^{2}}$

Step 2.6

One to any power is one.

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

Step 2.7

Add $1$ and $4$ .

$\sqrt{5 + 1 + 1 + 4 + 1}$

Step 2.8

Add $5$ and $1$ .

$\sqrt{6 + 1 + 4 + 1}$

Step 2.9

Add $6$ and $1$ .

$\sqrt{7 + 4 + 1}$

Step 2.10

Add $7$ and $4$ .

$\sqrt{11 + 1}$

Step 2.11

Add $11$ and $1$ .

$\sqrt{12}$

Step 2.12

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 2.12.1

Factor $4$ out of $12$ .

$\sqrt{4 (3)}$

Step 2.12.2

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

$\sqrt{2^{2} \cdot 3}$

Step 2.13

Pull terms out from under the radical.

$2 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{3}$

Decimal Form:

$3.46410161 \dots$