Linear Algebra Examples

$[\begin{array}{c} 0.4 & 1 \\ 0.6 & 0 \end{array}]$

Step 1

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

$\sqrt{{0.4}^{2} + 1^{2} + {0.6}^{2} + 0^{2}}$

Step 2

Simplify.

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Step 2.1

Raise $0.4$ to the power of $2$ .

$\sqrt{0.16 + 1^{2} + {0.6}^{2} + 0^{2}}$

Step 2.2

One to any power is one.

$\sqrt{0.16 + 1 + {0.6}^{2} + 0^{2}}$

Step 2.3

Raise $0.6$ to the power of $2$ .

$\sqrt{0.16 + 1 + 0.36 + 0^{2}}$

Step 2.4

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

$\sqrt{0.16 + 1 + 0.36 + 0}$

Step 2.5

Add $0.16 + 1 + 0.36$ and $0$ .

$\sqrt{0.16 + 1 + 0.36}$

Step 2.6

Add $0.16$ and $1$ .

$\sqrt{1.16 + 0.36}$

Step 2.7

Add $1.16$ and $0.36$ .

$\sqrt{1.52}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$\sqrt{1.52}$

Decimal Form:

$1.23288280 \dots$