I don't know about matrices, but this just looks like a simultaneous equation.

There might be a better way of solving this, but I'd do it like this:

Rearrange equation 3: B = 29 - 3A - 2C

Substitute into equation 2:

5A + 2(29 - 3A - 2C) - 4C = 37

A + 8C = 21

A = 21 - 8C

Substitute into equation 1:

5(21 - 8C) + 3(29 - 3(21 - 8C) - 2C) - 2C = 51

105 - 40C + 87 - 189 + 72C - 6C - 2C = 51

24C = 48

C = 2

Use C to find A:

A = 21 - 8*2 = 5

Use A and C to find B:

B = 29 - 3*5 - 2*2 = 10

So, **A = 5, B = 10, C = 2.**

As I said, there's probably an shorter way that I don't know about.