
linear combinations
let
A=
1 2
12
b=
4
0
c=
3
2
a) write b as a linear combination of the column vectors a1 and a2
b) use the result from a to determine solution of linear system Ax = b. does the system have any other solutions? explain.
c) write c as a linear combination of a1 and a2.
I got part a) I think
b = 2a1 +a2 since 2 times a1 plus one a2 equals the b matrix.
so then part b)
x would be
2
1
since
2 times A is b
1
c) is where I am stuck
I cant figure out a combination for
c=
3
2
I feel I need to subtract a2 from a1, but then the bottom position wont be 2 if I subtract a1 by 2a2

solve the two equations:
x2y = 2
x+2y = 3
then x will be what you multiply a1 by, and y will be what you multiply a2 by.
hint: they won't be integers.

Thanks. The TA for our class explained it the same way.
made a matrix and reduced it and got the solution.