Linear Algebra Examples

$[\begin{array}{c} 1 & 0 \\ 6 & - 1 \end{array}]$

Step 1

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

$\sqrt{1^{2} + 0^{2} + 6^{2} + {(- 1)}^{2}}$

Step 2

Simplify.

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Step 2.1

One to any power is one.

$\sqrt{1 + 0^{2} + 6^{2} + {(- 1)}^{2}}$

Step 2.2

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

$\sqrt{1 + 0 + 6^{2} + {(- 1)}^{2}}$

Step 2.3

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

$\sqrt{1 + 0 + 36 + {(- 1)}^{2}}$

Step 2.4

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

$\sqrt{1 + 0 + 36 + 1}$

Step 2.5

Add $1$ and $0$ .

$\sqrt{1 + 36 + 1}$

Step 2.6

Add $1$ and $36$ .

$\sqrt{37 + 1}$

Step 2.7

Add $37$ and $1$ .

$\sqrt{38}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{38}$

Decimal Form:

$6.16441400 \dots$