Find the​ B-coordinate vector of x (matrix)

Question

My vector $x$ is in a subspace $H$ with a basis $B = \{b1,b2\}$.

b1 = [ 5]      b2 = [-1]        x = [ 5]
     [-9]           [ 3]            [-3]

I need to find the​ B-coordinate vector of $x$.

I found out it is:

B-coordinate = [c1]
               [c2]

Where

[ 5] = c1[ 5] + c2[ -1]
[-3]     [-9]     [  3]

Problem is I don't know how to solve for c1 and c2 in such an equation?

Answer 1

You have to pull the factors c1 and c2 into your vectors. Then you get a simple linear system with 2 equations and two unknowns (c1 and c2).