Define t: r^2 rightarrow r with the property that t(x) = ax. find a basis b for r^2 with the property that [t]_b is diagonal. write the expression for [t]_b corresponding to b. a = [5 1 2 4] let the matrix a = [3 -20 1 11] act on c^2. find the eigenvalues and a basis for each eigen space in c^2.