Find the coordinate matrix of x in Rn relative to the basis

Find the coordinate matrix of x in Rn relative to the basis B. (Enter each vector as a comma-separated list of its components.)

B = {(8, 11, 0), (7, 0, 10), (1, 4, 6)}, x = (40, 48, 16)

Solution

Let, x=(40,48,16)=a(8,11,0)+b(7,0,10)+c(1,4,6)

40=8a+7b+c

48=11a+4c

16=10b+6c

Solving gives

a=4,b=1,c=1

So coordinates of x are : [4 1 1]^T