How to Express a Vector in Terms of Basis Vectors?

[939]

Homework Statement

Given the basis vector:

e1 = 1 0 0 0
e2 = 0 1 0 0
e3 = 0 0 1 0
e4 = 0 0 0 1

Express the following vector in terms of the basis:

y = 3 1 2 5

Homework Equations

e1 = 1 0 0 0
e2 = 0 1 0 0
e3 = 0 0 1 0
e4 = 0 0 0 1

y = 3 1 2 5

The Attempt at a Solution

= 3(e1) + 0.5(e2) + 2(e3) + 5(e4)

 

[LCKurtz]

Homework Statement

Given the basis vector:

e1 = 1 0 0 0
e2 = 0 1 0 0
e3 = 0 0 1 0
e4 = 0 0 0 1

Express the following vector in terms of the basis:

y = 3 1 2 5

Homework Equations

e1 = 1 0 0 0
e2 = 0 1 0 0
e3 = 0 0 1 0
e4 = 0 0 0 1

y = 3 1 2 5

The Attempt at a Solution

= 3(e1) + 0.5(e2) + 2(e3) + 5(e4)

Why the .5?

 

[Rellek]

Yeah, what he said ^^

 

[HallsofIvy]

(3, 1, 2, 5)= (3, 0, 0, 0)+ (0, 1, 0, 0)+ (0, 0, 2, 0)+ (0, 0, 0, 5)
= 3(1, 0, 0, 0)+ 1(0, 1, 0, 0)+ 2(0, 0, 1, 0)+ 5(0, 0, 0, 1)
= 3e1+ 1e2+ 2e3+ 5e4