# Linear Algebra questions and answers in March 2023

s. (1 point) Which of the following sets are subspaces of R.? JA. {(x,y,2) [xty+ 2=0} B. {(4, y, z) | y, z arbitrary numbers } c. {(x, y,z) atytz=7) Do. {(x, y, z) - 4x - 6y = 0, -9x -72 = 0} E. {(r, ... . 3. (1+3+2+4=10 points) Let N be the subspace of R4 consisting of vectors (:6, y, z, w) satisfying 2m—3y—z+w=0. (a) Consider the sets A = {(1,0,0,—2), (0,1,0,3), (0,0,1,1)} and B = {(—1,—... . Consider the bases B = {p1, p,} and B' = {q1, 92} for P1, where P1 = 8 + 7%, P, = 8 + 10x, q, = 2, q, =7+ 2x. Find the transition matrix from B to B'. 33 27 The transition matrix from B to B' is Q...