Linear Algebra Examples

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

Step 1

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

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

Step 2

Simplify.

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Step 2.1

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

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

Step 2.2

One to any power is one.

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

Step 2.3

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

$\sqrt{4 + 1 + 9 + {(- 1)}^{2}}$

Step 2.4

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

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

Step 2.5

Add $4$ and $1$ .

$\sqrt{5 + 9 + 1}$

Step 2.6

Add $5$ and $9$ .

$\sqrt{14 + 1}$

Step 2.7

Add $14$ and $1$ .

$\sqrt{15}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{15}$

Decimal Form:

$3.87298334 \dots$