Thread: Simple Linear Combination problem

I have 3 vectors a1, a2, a3 and then vector b. I want to write vector b as a linear combination of the 3 a vectors.

I create a matrix with the 3 a vectors and vector b on the right side. Then I reduce row the matrix.
Now I rewrite the reduced row echelon form and I isolate x1 and x2 and I rename x3 to the parameter "t".

I know insert the values of x1, x2 and x3 into my linear combination.

My problem is that when I choose a value for the parameter "t", I do not get the values from my b vector. But I have no idea what I've done wrong!
Can somebody help me and tell me what I did wrong?

it's probably just an arithmetic error, all your work is correct.

when we add the linear combinations we get:

((1+t)/2)(1,2) + ((1-3t)/2)(5,6) + t(7,8) = (((1+t)/2 + (5-15t)/2 + 7t), (1+t + 3-9t + 8t))

= ((6-14t)/2 + 7t, 4-8t + 8t) = (3 - 7t + 7t, 4 - 8t + 8t) = (3,4)

I see, thanks. :-)