1. ## Matrix Algebra help!

I need some help on this question and a couple explanations on some terms.

$A= \left(\begin{array}{cc}k&-2\\1-k&k\end{array}\right)$, where k is a constant.

A transformation $T: \Re^2 \rightarrow \Re^2$ is represented by the matrix A.

a) Find the value of k for which the line y=2x is mapped onto itself under T

b) show that A is non-singular for all values of k

i need help on both parts of the question, and waht is ment by non-singular?

2. Dear Stylis10,

hint a) let [y1 y2]' = A * [x 2x]'
the condition is y2/y1 = 2 for all x

hint b) A is non-singular means det(A)<>0