# Linear Algebra : Norms

## Example Questions

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### Example Question #1 : Norms

Find the norm of the following vector.

Explanation:

The norm of a vector is simply the square root of the sum of each component squared.

### Example Question #2 : Norms

Find the norm of vector .

Explanation:

In order to find the norm, we need to square each component, sum them up, and then take the square root.

### Example Question #3 : Norms

Find the norm, , given

Explanation:

By definition,

,

therefore,

.

### Example Question #4 : Norms

Calculate the norm of  , or , given

,

.

Can not be determined.

Explanation:

First, we need to find .  This is, by definition,

.

Therefore,

.

### Example Question #5 : Norms

Find the norm of the vector

Explanation:

To find the norm, square each component, add, then take the square root:

### Example Question #6 : Norms

Find a unit vector in the same direction as

Explanation:

First, find the length of the vector:

Because this vector has the length of 4 and a unit vector would have a length of 1, divide everything by 4:

### Example Question #7 : Norms

Find the norm of the vector

Explanation:

This can be simplified:

### Example Question #8 : Norms

Find the norm of the vector

Explanation:

### Example Question #9 : Norms

Find the norm of the vector

Explanation:

This can be simplified:

### Example Question #10 : Norms

Find the norm of the vector