(a) (2 points} Let S be a triangle in R2 with area 4. Let T(:r) = An: where A = (i 32). Find the area of T(S). (b) (2 points) Suppose A is a 3 x 3 positive stochastic matrix with the property that as n. 200 50 gets very large, A\" (300) approaches (50) . Find the constant k. 100 k (c) (3 points} Write a matrix A such that Co1(A) = Span { (g) } and Nul(A) = Span {(1) } . (d) (2 points} Give an example of a matrix that is invertible but not diagonalizable. (e) (3 points) Write a 2 X 3 matrix A in RREF such that the solution set to A9: = CI is a line. 2 l 2 c (f) (2 points) Find the value of r: so that c = ( 2 1 ) is an eigenvector of A = ( ). Find the corresponding eigenvalue as well. 4 1 to 1:. Briey show your work. 4 1 (g) (3 points) Let u = (3) , c = ( 2 ) . Find the value of k such that u+ he is orthogonal (h) (3 points} Suppose A,B are 2 x 2 matrices. If det(A) = 2 and det(B_1) = 8, nd det(4BAT}. Briey show your work