Answer:
See below
Step-by-step explanation:
Recall first:
Given a vector
[tex](x_1,x_2,...,x_n)[/tex]
Euclidean norm
[tex]\sqrt{x_1^2+x_2^2+...+x_n^2}[/tex]
Sum norm
[tex]|x_1|+|x_2|+...+|x_n|[/tex]
Max norm
[tex]Max\{|x_1|,|x_2|,...|x_n|\}[/tex]
Now let us apply these definitions to our vectors
Vector (1,1,1)
Euclidean norm
[tex]\sqrt{1^2+1^2+1^2}=\sqrt{3}[/tex]
Sum norm
|1|+|1|+|1| = 3
Max norm
Max{|1|, |1|, |1|} = |1| = 1
Vector (3,0,0)
Euclidean norm
[tex]\sqrt{3^2+0^2+0^2}=\sqrt{3^2}=3[/tex]
Sum norm
|3|+|0|+|0| = 3
Max norm
Max{|3|, |0|, |0|} = |3| = 3
Vector (-1,1,4)
Euclidean norm
[tex]\sqrt{(-1)^2+1^2+4^2}=\sqrt{18}[/tex]
Sum norm
|-1|+|1|+|4| = 1+1+4 =6
Max norm
Max{|-1|, |1|, |4|} = |4| = 4
Vector (-1.4, 3)
Euclidean norm
[tex]\sqrt{(-1.4)^2+3^2}=\sqrt{10.96}[/tex]
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
[tex]\sqrt{4^2+4^2+4^2+4^2}=\sqrt{4*4^2}=8[/tex]
Sum norm
|4|+|4|+|4|+|4| = 16
Max norm
Max{|4|, |4|, |4|, |4|} = |4| = 4
