Question

How do I solve this Matrix equation requiring inverses?

Answer 1

My guess is that I find the inverse of
-1 -9
0 -1
then multiply it by
11
2?

Answer 2

Please note I haven't learned this before and this is the way i'm going to learn it, but I have a strong grasp on matrix inverses and multiplication, etc

Answer 3

That's correct.

Answer 4

Nonhomogeneous matrix equations of the form
AX=B
can be solved by taking the matrix inverse to obtain
X=A^(-1) B
so u r right

Answer 5

Alright, sweet. However, I don't understand what AX=B means... or what nonhomogenous means?

Answer 6

ok

Answer 7

A is the matrix. X is the vector you're trying to solve for (C in your example) and B is the right hand side. In this case the column vector (11, 2) .

A homogeneous equation is one that looks like AX=0. Non-homogeneous is when the RHS is non-zero.

Answer 8

Thank you so much again :D. But what does the right hand side being zero have to do with anything? Why is it important?

Answer 9

When the right hand side is 0 you are guaranteed to have a solution (the 0 vector).

Sometimes you have an infinite number of solutions even for Ax=b. The way to find all of them is to find all the solutions for Ax*=0 and ONE particular solution for Ax=b. By adding that one x to each of the x* that solved the homogeneous equation you get all the solutions of the non-homogeneous equation.

Answer 10

One small note, you can't always solve these equations using inverses. A might not have an inverse even when the equation has a solution.

Actually, when there are infinitely many solutions the matrix A won't have an inverse.

Answer 11

I don't understand "The way to find all of them is to find all the solutions for Ax*=0 and ONE particular solution for Ax=b. "
Does that mean that the matrix I solved for, which is
7
-2
isn't a solution?? What do you mean by having an infinite number of solutions? And how would I solve it when A doesn't have an inverse?