- #1
bananasplit
- 9
- 0
Homework Statement
I have an idea on how to part 1, but I have no clue on how to do part 2 and 3.
1.Suppose A is invertible. Check that (A-1)TAT=I and AT(A-1)T=I, and deduce that AT is likewise invertible with inverse (A-1)T.
2. Suppose A is an mxn matrix with rank 1. Prove that there are nonzero vectors u element in Rm and v element in Rn such that A=uvT.
3.Suppose A is an mxn matrix and x is an element of Rn satisfies (ATA)x=0. Prove that AX=0.
Homework Equations
For part one I'm guessing (AB)T=BTAT and (A-1A-1)=I
The Attempt at a Solution
Part 1. I know that some kind of way that it is due to the relationship of (A-1A-1)=I