How can I find the values of each coefficient within a vector in a matrix multiplication problem?

Question

I have all the other T and alpha values and I'm trying to solve for a0 a1 and a2

I can't simply divide them

so I figure in need to do something like this

But i'm not sure how to go about it? What's this called? Do I substitute all the a, a1, a2 values for one another? Can someone just tell me what kind of problem this is so I may have better luck googling? Thank you.

In your link I assume the following would yield the answer:

but I don't know how to compute what appears to be one matrix divided by another [Matrix]/[Matrix] What's that called?

Regardless following this video to find A^-1 and then multiplying that by B like in this other video will give me what I want yes? ( a0, a1, a2 )

Answer 1

On your $A\cdot X=B$ problem, if you know the matrix $A$ and the right vector $B$, then the solution is simply $X = A^{-1}\cdot B$. Or did I missed something ?

Or if you really want to play manually with the system of equations, there is the classical Gauss-Jordan elimination trick, combining lines togethers to create zeros in the matrix, up to the point it becomes trivial to solve (triangular, or even diagonal).