Q:

Why if the rank of matrix $M=\begin{pmatrix}2x&2y&0\\1&0&1\\ \end{pmatrix}$ is less than $2$,then $x=y=0$?

The rank of matrix $M=\begin{pmatrix}2x&2y&0\\1&0&1\\ \end{pmatrix}$ is less than $2$ if and only if $x=y=0$.

I can't understand the only if part, that is why "if the rank of matrix $M=\begin{pmatrix}2x&2y&0\\1&0&1\\ \end{pmatrix}$ is less than $2$,then $x=y=0$"?

A:

Perhaps it is easier to understand in the negative. "If either $x$ or $y$ is nonzero, the rank of the matrix is 2." You can work that out, I think.

