Linear Algebra Examples

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

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

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}}

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

Step 2

Simplify.

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Step 2.1

One to any power is one.

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

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

Step 2.2

Raising

0

$0$ to any positive power yields

0

$0$ .

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

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

Step 2.3

Raise

6

$6$ to the power of

2

$2$ .

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

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

Step 2.4

Raise

- 1

$- 1$ to the power of

2

$2$ .

\sqrt{1 + 0 + 36 + 1}

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

Step 2.5

Add

1

$1$ and

0

$0$ .

\sqrt{1 + 36 + 1}

$\sqrt{1 + 36 + 1}$

Step 2.6

Add

1

$1$ and

36

$36$ .

\sqrt{37 + 1}

$\sqrt{37 + 1}$

Step 2.7

Add

37

$37$ and

1

$1$ .

\sqrt{38}

$\sqrt{38}$

\sqrt{38}

$\sqrt{38}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\sqrt{38}

$\sqrt{38}$

Decimal Form:

6.16441400 \dots

$6.16441400 \dots$