Let $T$ is a linear transformation on $\mathbb{R}^2$. $x,y$ linearly indipendent vector in $\mathbb{R}^2$, $T(y)=\alpha x$ and $T(x)=0$, Then with respect to some basis in $\mathbb{R}^2$, $T$ is of the form...
$\pmatrix{a&0\\0&a},\;a>0$
$\pmatrix{a&0\\0&b},\;a,b>0,a\ne b$
$\pmatrix{0&1\\0&0}$
$\pmatrix{0&0\\0&0}$
I have calculated the answer to be 3. Can anyone verify this?