Matrices to solve a vector combination problem.

I am completely confused by your notation…

Your very first equation doesn’t make sense. In Matrix Addition, the sum matrix is comprised of the sums of the corresponding elements of the original matrices.

|3| |2| |5|
| |+| |=| |
|-6||6| |0|

That is, the matrix of 3 over -6 plus the matrix of 2 over 6 equals the matrix of 5 over 0, not 7 over 6.

X=1
Y=2

That is, assuming you’ve simply represented linear simultaneous equations:

3X + 2Y = 7
-6X + 6Y = 6,

which can we rewritten in matrix form:

| 3 2 | |X| = |7|
|-6 6 | |Y| = |6|, where this is basically in the form: [A][B] = [C].

Rewriting, you can use inv[A][C] = [B], which solves the linear system using inverse matrices.

A much easier way to do this is through simple elimination (or even substitution). For instructions on that, please see 7th Grade.