# Linear Algebra Examples

,

Step 1

The distance between two vectors and in is defined to be which is the Euclidean norm of the difference .

Step 2

Step 2.1

Create a vector of the difference.

Step 2.2

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

Step 2.3

Simplify.

Step 2.3.1

Subtract from .

Step 2.3.2

Raising to any positive power yields .

Step 2.3.3

Subtract from .

Step 2.3.4

Raise to the power of .

Step 2.3.5

Add and .

Step 2.3.6

Raise to the power of .

Step 2.3.7

Add and .

Step 2.3.8

Add and .

Step 3

The result can be shown in multiple forms.

Exact Form:

Decimal Form: