Linear Algebra Examples

$- 3 A = [\begin{array}{c} - 9 & - 1 \\ - 2 & - 3 \end{array}]$

Step 1

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

$\sqrt{{(- 9)}^{2} + {(- 1)}^{2} + {(- 2)}^{2} + {(- 3)}^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $- 9$ to the power of $2$ .

$\sqrt{81 + {(- 1)}^{2} + {(- 2)}^{2} + {(- 3)}^{2}}$

Step 2.2

Raise $- 1$ to the power of $2$ .

$\sqrt{81 + 1 + {(- 2)}^{2} + {(- 3)}^{2}}$

Step 2.3

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

$\sqrt{81 + 1 + 4 + {(- 3)}^{2}}$

Step 2.4

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

$\sqrt{81 + 1 + 4 + 9}$

Step 2.5

Add $81$ and $1$ .

$\sqrt{82 + 4 + 9}$

Step 2.6

Add $82$ and $4$ .

$\sqrt{86 + 9}$

Step 2.7

Add $86$ and $9$ .

$\sqrt{95}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{95}$

Decimal Form:

$9.74679434 \dots$