Linear Algebra Examples

$[\begin{array}{c} 3 & - 3 & - 6 & - 3 \\ 2 & - 2 & - 4 & h \\ - 2 & 3 & - 4 & 7 \end{array}]$

Step 1

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

$\sqrt{3^{2} + {(- 3)}^{2} + {(- 6)}^{2} + {(- 3)}^{2} + 2^{2} + {(- 2)}^{2} + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{9 + {(- 3)}^{2} + {(- 6)}^{2} + {(- 3)}^{2} + 2^{2} + {(- 2)}^{2} + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.2

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

$\sqrt{9 + 9 + {(- 6)}^{2} + {(- 3)}^{2} + 2^{2} + {(- 2)}^{2} + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.3

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

$\sqrt{9 + 9 + 36 + {(- 3)}^{2} + 2^{2} + {(- 2)}^{2} + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.4

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

$\sqrt{9 + 9 + 36 + 9 + 2^{2} + {(- 2)}^{2} + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.5

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

$\sqrt{9 + 9 + 36 + 9 + 4 + {(- 2)}^{2} + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.6

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

$\sqrt{9 + 9 + 36 + 9 + 4 + 4 + {(- 4)}^{2} + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.7

Raise $- 4$ to the power of $2$ .

$\sqrt{9 + 9 + 36 + 9 + 4 + 4 + 16 + h^{2} + {(- 2)}^{2} + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.8

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

$\sqrt{9 + 9 + 36 + 9 + 4 + 4 + 16 + h^{2} + 4 + 3^{2} + {(- 4)}^{2} + 7^{2}}$

Step 2.9

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

$\sqrt{9 + 9 + 36 + 9 + 4 + 4 + 16 + h^{2} + 4 + 9 + {(- 4)}^{2} + 7^{2}}$

Step 2.10

Raise $- 4$ to the power of $2$ .

$\sqrt{9 + 9 + 36 + 9 + 4 + 4 + 16 + h^{2} + 4 + 9 + 16 + 7^{2}}$

Step 2.11

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

$\sqrt{9 + 9 + 36 + 9 + 4 + 4 + 16 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.12

Add $9$ and $9$ .

$\sqrt{18 + 36 + 9 + 4 + 4 + 16 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.13

Add $18$ and $36$ .

$\sqrt{54 + 9 + 4 + 4 + 16 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.14

Add $54$ and $9$ .

$\sqrt{63 + 4 + 4 + 16 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.15

Add $63$ and $4$ .

$\sqrt{67 + 4 + 16 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.16

Add $67$ and $4$ .

$\sqrt{71 + 16 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.17

Add $71$ and $16$ .

$\sqrt{87 + h^{2} + 4 + 9 + 16 + 49}$

Step 2.18

Add $87$ and $4$ .

$\sqrt{h^{2} + 91 + 9 + 16 + 49}$

Step 2.19

Add $91$ and $9$ .

$\sqrt{h^{2} + 100 + 16 + 49}$

Step 2.20

Add $100$ and $16$ .

$\sqrt{h^{2} + 116 + 49}$

Step 2.21

Add $116$ and $49$ .

$\sqrt{h^{2} + 165}$