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?