- #1
rofln
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Homework Statement
My instructor wants to know if there are finite or infinite amount of solutions
Homework Equations
Matrix Multiplication
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?