Linear Algebra Examples

[\begin{matrix} - 3 & 0 & - 6 - 2 & 3 & 4 \end{matrix}]

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

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}}

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

Step 2

Simplify.

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Step 2.1

Raise

- 3

$- 3$ to the power of

2

$2$ .

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

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

Step 2.2

Raising

0

$0$ to any positive power yields

0

$0$ .

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

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

Step 2.3

Raise

- 6

$- 6$ to the power of

2

$2$ .

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

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

Step 2.4

Raise

- 2

$- 2$ to the power of

2

$2$ .

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

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

Step 2.5

Raise

3

$3$ to the power of

2

$2$ .

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

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

Step 2.6

Raise

4

$4$ to the power of

2

$2$ .

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

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

Step 2.7

Add

9

$9$ and

0

$0$ .

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

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

Step 2.8

Add

9

$9$ and

36

$36$ .

\sqrt{45 + 4 + 9 + 16}

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

Step 2.9

Add

45

$45$ and

4

$4$ .

\sqrt{49 + 9 + 16}

$\sqrt{49 + 9 + 16}$

Step 2.10

Add

49

$49$ and

9

$9$ .

\sqrt{58 + 16}

$\sqrt{58 + 16}$

Step 2.11

Add

58

$58$ and

16

$16$ .

\sqrt{74}

$\sqrt{74}$

\sqrt{74}

$\sqrt{74}$

Step 3

The result can be shown in multiple forms.

Exact Form:

\sqrt{74}

$\sqrt{74}$

Decimal Form:

8.60232526 \dots

$8.60232526 \dots$