Question

10. Deteruine whet her from the spanning set 11. Given the matrix W 0 3 0 21 2 (a) Fad all the eigeuvahues of W (b) Fmd all e苇e:nvectorsofg (c) Is the muatrix W' dagoaalizable? If YES, wate a factoritraion f the matrix in the form P DP. IINO, explain why. 110 ill and Tello 1 11 11 0明1 įì 12. Let Ss(111 1] , [l 2 31 11} be sets of -3 (a) Find the vertor u ifas coordinates with respect to the set of ordered base T ur = (b) Fiad the transition suatrix Pst from the set of ordered basis T to the set d adered basis S (c) Use the transtion matrix Ps-r yn wish, to fad the coordinates of the vector [uls with respect to the set of ordered basis S

Answer 1

"Given S = {[-1 1 1 -1], [1 1 1 1], [1 0 0 1], [0 1 1 0]} Dimension of M_22 is 4 above set S spans M_22 iff S is linearly independent set but we observe that [-1 1 1 -1] + [1 0 0 1] = [-1 + 1 1 1 -1 + 1] = [0 1 1 0] \r\n doublerightarrow [0 1 1 0] is a linear combination of [-1 1 1 -1] & [1 0 0 1] doublerightarrow S is linearly dependent set doublerightarrow S does not span M_22 (ii) given matrix is w = [-3 0 -2 -1 3 -1 -3 0 -2] (a) The characteristics equations is det (w - lambda I) = 0