Question

2. Give the euclidean norm, sum norm, and max norm of the. fallowing vectors. (a) (1, 1, l] (b) [3,0,0] (c) [-1, 1,4] (d) ( - 1.4, 3] (e) [4, 4, 4, 4]

Answer 1

See below

Explanation:

Recall first:

Given a vector

`(x_1,x_2,...,x_n)`

Euclidean norm

`√(x_1^2+x_2^2+...+x_n^2)`

Sum norm

`|x_1|+|x_2|+...+|x_n|`

Max norm

`Max\x_n`

Now let us apply these definitions to our vectors

Vector (1,1,1)

Euclidean norm

`√(1^2+1^2+1^2)=√(3)`

Sum norm

|1|+|1|+|1| = 3

Max norm

Max1 = |1| = 1

Vector (3,0,0)

Euclidean norm

`√(3^2+0^2+0^2)=√(3^2)=3`

Sum norm

|3|+|0|+|0| = 3

Max norm

Max0 = |3| = 3

Vector (-1,1,4)

Euclidean norm

`√((-1)^2+1^2+4^2)=√(18)`

Sum norm

|-1|+|1|+|4| = 1+1+4 =6

Max norm

Max-1 = |4| = 4

Vector (-1.4, 3)

Euclidean norm

`√((-1.4)^2+3^2)=√(10.96)`

Sum norm

|-1.4|+|3| = 1.4+3 = 4.4

Max norm

Max, = |3| = 3

Vector (4,4,4,4)

Euclidean norm

`√(4^2+4^2+4^2+4^2)=√(4*4^2)=8`

Sum norm

|4|+|4|+|4|+|4| = 16

Max norm

Max, = |4| = 4