Let $T:\Bbb R^2\to \Bbb R^2$ be a linear transformation such that $T (1,1)=(9,2)$ and $T(2,-3)=(4,-1)$.
A) Determine if the vectors $(1,1)$ and $(2,-3)$ form a basis.
B) Calculate $T(x,y)$.
I need help with these, please I'm stuck, don't even know how to start them…
Best Answer
You can't scalair multiply $(1,1)$ to get $(2, -3)$, so the vectors are linear independent. So the span of these vectors are a basis for $\mathbb{R^2}$ (dimension is also ok).