
Matrix Algebra help!
I need some help on this question and a couple explanations on some terms.
$\displaystyle A= \left(\begin{array}{cc}k&2\\1k&k\end{array}\right)$, where k is a constant.
A transformation $\displaystyle T: \Re^2 \rightarrow \Re^2$ 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 nonsingular for all values of k
i need help on both parts of the question, and waht is ment by nonsingular?

Dear Stylis10,
hint a) let [y1 y2]' = A * [x 2x]'
the condition is y2/y1 = 2 for all x
hint b) A is nonsingular means det(A)<>0