Question

Let T: R^2 -> R^2 be a linear transformation such that T(i) = (3 2) and T(j) = (-6 -4)
Find a matrix that induces T
Is T invertible?

Answer 1

T(i) = \[\left(\begin{matrix}3 \\ 2\end{matrix}\right)\]
T(j) = \[\left(\begin{matrix}-6 \\ -4\end{matrix}\right)\]

Answer 2

Not too clear on the notation, I will guess that u want
\[\left( \begin{array}{cc} 3 & -6 \\ 2 & -4 \end{array} \right)\]

which will map(i,j) to (3i -6j,2i-4j) = i(3,2) +j(-6,-4)

Since the determinant is not 0, this transformation is invertible.

Answer 3

(3*-4)-(2*(-6))=0

Answer 4

Oops, quite right, so not invertible:-)