1. The problem statement, all variables and given/known data The problem is to decide that the vector v = (2, -7, 1) lies in the same plane M as the vectors u1 = (2, -1, 3) and u2 = (1, 1 ,2) and express v as coordinates in the base u1, u2 2. Relevant equations I decided to utilize that if the three vetors lies in the same plane, they must be linear dependent. If we assume that u1 and u2 lies in the same plane as v then we can express v as: v = s1u1 + s2u2 Then s1u1 + s2u2 - s3v = 0 If they are linearily dependent they must lie in the same plane. Right? 3. The attempt at a solution I solved the linear equation that the above relationship gives and finds that one of the equations is 0 = 0, hence it has infinitely many solutions, i.e s1 and s2 can be arbitraily chosen. (Right?) I could now write v as coordinates in u1 and u2 By solving s1u1 + s2u2 = (2, -7, 1) for s1 and s2. I got the answer v = 3u1 - 4u2 Which was correct, according to the book. Now, i would like to know if this is a correct way to solve this problem, or if i was just getting lucky. This is my first attempt att liear algebra so I have no good intuition about the methods to solve this types of problems. Please be as critical as you can! Please point out any faults or "fuzzy thinking" I've done :) Happy New Years!! P.s Thanks in advance!