1.Suppose a 3x3 matrix has two eigenvalues: . The eigenspace for is one-dimensional, and the eigenspace for is two-dimensional. Note that vector lies on the plane created by and lies on the line created by , as illustrated in the graph below.

Choose the correct answer and explain: Suppose a 3x3 matrix B has two eigenvalues: 1 = 2, 1 = 4. The eigenspace E, for A = 2 is one-dimensional, and the eigenspace E, for 1 = 4 is two-dimensional. Note that vector x 6 R3 lies on the plane created by E, and y E 13 lies on the line created by E,. as illustrated in the graph below. E 2 2- 2 hefor have or Ing Z= y + 0.5x stretch 21 - place EA all sheech by 4 If z = y + 0.5x, which of the following is true? a) The vector z is an eigenvector of B with an eigenvalue of [fill in the blank] b) The vector z is not an eigenvector of B