Suppose A is a $m \times n$ matrix and the vectors $x$ and $y$ are such that $Az=y$ for some vector $z$ and $A^T x=0$. Which one is correct?
- $x^Ty=0$
- $||x||_2=||y||_2$
- $||x||_2 < ||y||_2$
- $x=ay$ for some real values of $a$
Suppose A is a $m \times n$ matrix and the vectors $x$ and $y$ are such that $Az=y$ for some vector $z$ and $A^T x=0$. Which one is correct?
So there's an answer...
(1) is the correct choice.
$x^Ty=x^TAz=x^T(A^T)^Tz=(A^Tx)^Tz=0z=0$