Linear Algebra Examples

$[\begin{array}{c} x & 2 & 3 & 4 & 5 & 6 \\ y & - 1 & 1 & 3 & 5 & 7 \end{array}]$

Step 1

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

$\sqrt{x^{2} + 2^{2} + 3^{2} + 4^{2} + 5^{2} + 6^{2} + y^{2} + {(- 1)}^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2

Simplify.

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Step 2.1

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

$\sqrt{x^{2} + 4 + 3^{2} + 4^{2} + 5^{2} + 6^{2} + y^{2} + {(- 1)}^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2.2

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

$\sqrt{x^{2} + 4 + 9 + 4^{2} + 5^{2} + 6^{2} + y^{2} + {(- 1)}^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2.3

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

$\sqrt{x^{2} + 4 + 9 + 16 + 5^{2} + 6^{2} + y^{2} + {(- 1)}^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2.4

Raise $5$ to the power of $2$ .

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 6^{2} + y^{2} + {(- 1)}^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2.5

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

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 36 + y^{2} + {(- 1)}^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2.6

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

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 36 + y^{2} + 1 + 1^{2} + 3^{2} + 5^{2} + 7^{2}}$

Step 2.7

One to any power is one.

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 36 + y^{2} + 1 + 1 + 3^{2} + 5^{2} + 7^{2}}$

Step 2.8

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

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 36 + y^{2} + 1 + 1 + 9 + 5^{2} + 7^{2}}$

Step 2.9

Raise $5$ to the power of $2$ .

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 36 + y^{2} + 1 + 1 + 9 + 25 + 7^{2}}$

Step 2.10

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

$\sqrt{x^{2} + 4 + 9 + 16 + 25 + 36 + y^{2} + 1 + 1 + 9 + 25 + 49}$

Step 2.11

Add $4$ and $9$ .

$\sqrt{x^{2} + 13 + 16 + 25 + 36 + y^{2} + 1 + 1 + 9 + 25 + 49}$

Step 2.12

Add $13$ and $16$ .

$\sqrt{x^{2} + 29 + 25 + 36 + y^{2} + 1 + 1 + 9 + 25 + 49}$

Step 2.13

Add $29$ and $25$ .

$\sqrt{x^{2} + 54 + 36 + y^{2} + 1 + 1 + 9 + 25 + 49}$

Step 2.14

Add $54$ and $36$ .

$\sqrt{x^{2} + 90 + y^{2} + 1 + 1 + 9 + 25 + 49}$

Step 2.15

Add $90$ and $1$ .

$\sqrt{x^{2} + y^{2} + 91 + 1 + 9 + 25 + 49}$

Step 2.16

Add $91$ and $1$ .

$\sqrt{x^{2} + y^{2} + 92 + 9 + 25 + 49}$

Step 2.17

Add $92$ and $9$ .

$\sqrt{x^{2} + y^{2} + 101 + 25 + 49}$

Step 2.18

Add $101$ and $25$ .

$\sqrt{x^{2} + y^{2} + 126 + 49}$

Step 2.19

Add $126$ and $49$ .

$\sqrt{x^{2} + y^{2} + 175}$