Answer
$T(1,4)=(-3,5)\\
T(-2,1)=(-3,-1)$
Work Step by Step
Observe that $(1,4)=1(1,0)+4(0,1)$
Since, $T$ is a linear transformation,
$T(1,4)\\=T[1(1,0)+4(0,1)]\\=1T(1,0)+4T(0,1)\\
=(1,1)+4(-1,1)\\
=(-3,5)$
Now, observe that $(-2,1)=(-2)(1,0)+1(0,1)$
Since, $T$ is a linear transformation,
$T(-2,1)\\=T[(-2)(1,0)+1(0,1)]\\=(-2)T(1,0)+1T(0,1)\\
=(-2)(1,1)+1(-1,1)\\
=(-3,-1)$