Question

Questions

1. Which real numbers do not have multiplicative inverses? What types of square matrices do not have inverses?

2. If A is an n by n matrix which has an inverse, if X is n by 1 and B is n by 1, explain how to solve the matrix equation AX = B for X.

3. How would you solve the matrix equation XA=B for X if X is 1 by n, A is n by n and has an inverse, and B is 1 by n?

Answer 1

1 singular matrices don't have inverse
2 if AX=B, then \[A^{-1}AX=A^{-1}B\]
\[X=A^{-1}B\]
3 Same as 2, when you move x, it'll be 1xn times nxn so it works out. But POST multiply
\[XAA^{-1}=BA^{-1}\]
\[X=BA^{-1}\]