Question

help with linear algebra?

Answer 1

3) T(e1) = e1-3e2
T(e2) = e2
--> matrix T =\(\left[\begin{matrix} 1&0\\-3&1\end{matrix}\right]\)
that is it

Answer 2

I'm a bit confused how to get there

Answer 3

the matrix A=[ T(e1) T(e2) ] right?

Answer 4

look at the coordinate of the right hand side, coordinate of e1 is 1, that is a11 in matrix

Answer 5

ok, let go shortcut;
\[\left[\begin{matrix} 1&0\\-3&1\end{matrix}\right]*\left[\begin{matrix} 1\\0\end{matrix}\right]=\left[\begin{matrix} 1\\-3\end{matrix}\right]\]
[T] (e1) = 1e1 -3e2 right??

Answer 6

because