1- Consider the system of difference equation Xk+1 = A Xk ; X0 = [1,1,1]T and A = [1, 2, 0; 2, 1, 0; 0, 0, 1].

[answerhappygod]

1- Consider the system of difference equation Xk+1 = A Xk ; X0 = [1,1,1]T and A = [1, 2, 0; 2, 1, 0; 0, 0, 1]. (A is symmetric).
· Is A diagonalizable? Why?
· Find X100 . (A matrix equation is sufficient)
2- Consider the matrix B = ATA; matrix A from problem 1. (5points)
· Is B positive definite? Why?
· XTBX = 1 is an ellipsoid in (x1 , x2 , x3) plane. Transfer the ellipse to Y = (y1 , y2 , y3) coordinates such that the axes of the ellipse fall along the coordinate axes