Linear Algebra Examples

$[\begin{array}{c} 3 & 6 & 0 & 9 & 8 & 7 \end{array}]$

Step 1

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

$\sqrt{3^{2} + 6^{2} + 0^{2} + 9^{2} + 8^{2} + 7^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{9 + 6^{2} + 0^{2} + 9^{2} + 8^{2} + 7^{2}}$

Step 2.2

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

$\sqrt{9 + 36 + 0^{2} + 9^{2} + 8^{2} + 7^{2}}$

Step 2.3

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

$\sqrt{9 + 36 + 0 + 9^{2} + 8^{2} + 7^{2}}$

Step 2.4

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

$\sqrt{9 + 36 + 0 + 81 + 8^{2} + 7^{2}}$

Step 2.5

Raise $8$ to the power of $2$ .

$\sqrt{9 + 36 + 0 + 81 + 64 + 7^{2}}$

Step 2.6

Raise $7$ to the power of $2$ .

$\sqrt{9 + 36 + 0 + 81 + 64 + 49}$

Step 2.7

Add $9$ and $36$ .

$\sqrt{45 + 0 + 81 + 64 + 49}$

Step 2.8

Add $45$ and $0$ .

$\sqrt{45 + 81 + 64 + 49}$

Step 2.9

Add $45$ and $81$ .

$\sqrt{126 + 64 + 49}$

Step 2.10

Add $126$ and $64$ .

$\sqrt{190 + 49}$

Step 2.11

Add $190$ and $49$ .

$\sqrt{239}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{239}$

Decimal Form:

$15.45962483 \dots$