# Math Help - linear combination

1. ## linear combination

Given v = [2] and w = [2]. Write [1] as a linear combination of v and w.
1 1 0
Just started the chapter. Help please???
I can't do it here. But number belong in the same bracket.

2. [1]=(1/2)v+(1/2)w

3. I did it wrong. It's supposed to be v=[2,1] where in actuality, 1 is at the bottom of 2. and w =[2, 1] where in actuality,1 is at the bottom of 2. Write [1,0] where in actuality, 0 is at the bottom of 1, as a linear combination of v and w. Can you please show the steps?

4. So v=w? strange... anyway...

Solve:

t[2,1]+r[2,1]=[1,0]

(t+r)[2,1]=[1,0]

2t+2r=1
t+r=0

or

t+r=1/2
t+r=0

1/2=0

impossible! Hence such t and r aren't exist .

Different way: w=v=[2,1]

s[2,1]=[1,0]

2s=1
s=0

the same conclusion!