Compute the product C ⃗s , and show that it is equal to the linear combination of ⃗c1, ⃗c2, and ⃗c3 with coefficients a, b, and c.

Question

Let c1, ⃗c2, ⃗c3, and ⃗s be the columns given below. Let C be the matrix C = [ ⃗c1 ⃗c2 ⃗c3]. That is, C is the matrix with columns ⃗c1, ⃗c2, and ⃗c3, in that order.

⃗c1 =

[1]

[2]

[3]

⃗c2 =

[0]

[1]

[-2]

⃗c3 =

[2]

[0]

[0]

⃗s =

[a]

[b]

[c] Compute the product C ⃗s , and show that it is equal to the linear combination of ⃗c1, ⃗c2, and ⃗c3 with coefficients a, b, and c.

also i don't know why it's not showing the arrow on top on the other c1s, c2s, c3s and s so just assume it's there

Answer 1

What you want to show is that C*s = a*c1 + b*c2 + c*c3. To show this we will need to perform the multiplication. Note that C*s will be a column vector with 3 elements.

The first element is computed as follows

a*1+b*0+c*2,

The second element is

a*2 +b*1+c*0

AND the third element is

a*3 + b*(-2) + c*0

But note as you move down the column you have a*1, then a*2 then a*3, but this is just a*c1, and you can see that it is similar for c2 and c3.