Question

How do you multiply 2x2 matrix [e^t, e^t, e^-t, 3e^-t] with [t^2, 0]? e^t and e^t on left, e^-t and 3e^-t on right, t^2 on top, 0 on bottom.

Answer 1

\[\left[\begin{matrix}e^t&e^{-t}\\e^t&3e^{-t}\end{matrix}\right]\left[\begin{matrix}t^2\\0\end{matrix}\right]\]

Answer 2

Yes.

Answer 3

you have 2x2 matrix time 2x1 matrix. the product supposedly is a 2x1 matrix, got it?