Linear Algebra Examples

$[\begin{array}{c} - 3 & 0 & - 6 \\ - 2 & 3 & 4 \end{array}]$

Step 1

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

$\sqrt{{(- 3)}^{2} + 0^{2} + {(- 6)}^{2} + {(- 2)}^{2} + 3^{2} + 4^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{9 + 0^{2} + {(- 6)}^{2} + {(- 2)}^{2} + 3^{2} + 4^{2}}$

Step 2.2

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

$\sqrt{9 + 0 + {(- 6)}^{2} + {(- 2)}^{2} + 3^{2} + 4^{2}}$

Step 2.3

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

$\sqrt{9 + 0 + 36 + {(- 2)}^{2} + 3^{2} + 4^{2}}$

Step 2.4

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

$\sqrt{9 + 0 + 36 + 4 + 3^{2} + 4^{2}}$

Step 2.5

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

$\sqrt{9 + 0 + 36 + 4 + 9 + 4^{2}}$

Step 2.6

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

$\sqrt{9 + 0 + 36 + 4 + 9 + 16}$

Step 2.7

Add $9$ and $0$ .

$\sqrt{9 + 36 + 4 + 9 + 16}$

Step 2.8

Add $9$ and $36$ .

$\sqrt{45 + 4 + 9 + 16}$

Step 2.9

Add $45$ and $4$ .

$\sqrt{49 + 9 + 16}$

Step 2.10

Add $49$ and $9$ .

$\sqrt{58 + 16}$

Step 2.11

Add $58$ and $16$ .

$\sqrt{74}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{74}$

Decimal Form:

$8.60232526 \dots$