1. The problem statement, all variables and given/known data My instructor wants to know if there are finite or infinite amount of solutions 2. Relevant equations Matrix Multiplication 3. The attempt at a solution I pretty much turned A into a 3x3 matrix like this... | A11 A12 A13 | | A21 A22 A23 | | A31 A32 A33 | and then multiplied it by the given matrix of x y and z. After multiplying I found myself with 2 matrices that I think would fit the solution... | y 0 0 | | 0 0 0 | | 0 0 0 | and | 0 x 0 | | 0 0 0 | | 0 0 0 | The first matrix would correspond to xy + 0y + 0z 0x + 0y + 0z 0x + 0y + 0z yielding the answer indicated by the question and the second would correspond to 0x + xy + 0z 0x + 0y + 0z 0x + 0y + 0z yielding the answered indicated by the question However, I find myself second guessing myself. I think I have 2 solutions, but since x and y are variables, they could be any number, ergo have infinite matrices. I think I may be over complicating things or perhaps I am just incorrect. Pretty much my question is, am I correct or perhaps on the right track or just wrong?