Linear Algebra Examples

$[\begin{array}{c} 2 & 6 \\ - 4 & - 12 \end{array}]$

Step 1

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

$\sqrt{2^{2} + 6^{2} + {(- 4)}^{2} + {(- 12)}^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{4 + 6^{2} + {(- 4)}^{2} + {(- 12)}^{2}}$

Step 2.2

Raise $6$ to the power of $2$ .

$\sqrt{4 + 36 + {(- 4)}^{2} + {(- 12)}^{2}}$

Step 2.3

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

$\sqrt{4 + 36 + 16 + {(- 12)}^{2}}$

Step 2.4

Raise $- 12$ to the power of $2$ .

$\sqrt{4 + 36 + 16 + 144}$

Step 2.5

Add $4$ and $36$ .

$\sqrt{40 + 16 + 144}$

Step 2.6

Add $40$ and $16$ .

$\sqrt{56 + 144}$

Step 2.7

Add $56$ and $144$ .

$\sqrt{200}$

Step 2.8

Rewrite $200$ as $10^{2} \cdot 2$ .

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Step 2.8.1

Factor $100$ out of $200$ .

$\sqrt{100 (2)}$

Step 2.8.2

Rewrite $100$ as $10^{2}$ .

$\sqrt{10^{2} \cdot 2}$

Step 2.9

Pull terms out from under the radical.

$10 \sqrt{2}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$10 \sqrt{2}$

Decimal Form:

$14.14213562 \dots$