. (2 points) Is { i (1}), (i 3) , (3 31) , (i 2)} a basis for the vector space ofall 2X2 matrices? Explain. . (2 points) Is {x 2, 3x2 + 1, x2 + x + 3} a basis for the vector space P2? Explain. . (3 points) Find a basis for and the dimension of all subspace of all 3x3 upper triangular matrices. . (3 points) Find a basis for and the dimension of the following subspace of R4 : {(33, t, s, s + 3t): 5' and t are real numbers} . (10 points) Given B = {(1,2,4), (1,2,0) , (2,4,0)} and B' = {(02.1) , (2,1,0) , (1,1,1)}, nd the following: a. The transition matrix from B to B' b. The transition matrix from B' to B. c. [55],; and [3213! for a? = (5,6,8) (:1. [y and [3213 for 55 = (1,2,3)