Find all values of c1 and c2 such that: c1(2, 2, 1) + c2(1,-2,2) = (3,6,0)

Answer 1

Distribute c1 into the first point and c2 into the second point, then add the two points together. Matching the x,y, and z components of the resulting point with the point on the right hand side gives the three following equations

2c1+c2=3

2c1-2c2=6

c1+2c2=0

Which implies the matrix

[2 1 3

2 -2 6

1 2 0]

Reduce this matrix and you'll have your answer, if it exists.