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]

See below

Step-by-step explanation:

Recall first:

Given a vector  

Euclidean norm

Sum norm

Max norm

Now let us apply these definitions to our vectors

Vector (1,1,1)

Euclidean norm

Sum norm

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

Max norm

Max{|1|, |1|, |1|} = |1| = 1

Vector (3,0,0)

Euclidean norm

Sum norm

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

Max norm

Max{|3|, |0|, |0|} = |3| = 3

Vector (-1,1,4)

Euclidean norm

Sum norm

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

Max norm

Max{|-1|, |1|, |4|} = |4| = 4

Vector (-1.4, 3)

Euclidean norm

Sum norm

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

Max norm

Max{|-1.4|, |3|} = |3| = 3

Vector (4,4,4,4)

Euclidean norm

Sum norm

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

Max norm

Max{|4|, |4|, |4|, |4|} = |4| = 4