Question

(1 point) Consider the ordered bases B = a. Find the transition matrix from C to B. 3 01 To Olmedi 011-3 0. *1 for the vector space V of lower triangular 2 x 2 matrices with zero trace. 3 4 01) and C=-5 -1/'1-23] b. Find the coordinates of M in the ordered basis B if the coordinate vector of M in C is M c [ MB = C. Find M. M =

Answer 1

The answers to a, b, c have been indicated with a red underline.

Solution B= { [30], 2007 = { bq, b₂} 610-31 140 NW o 22-5-1 2 -2 3. J a Transition matrix from C to B. TB - [T, TI where T, = [c, IB , Tz = [cz] B i e. [ci] B is matrix C, intams a basis B ů = 1,2 Lela-10-13:1- E5-1 R 320-3 ] 4 [40] - 1 b, - 15 bz -514 ::T, = [c, JB - 11 Ela-E:--13:1607 =-b, - I be T = [₂ B -17 - .: TB =[T, T2] = 1/3 -1 1-514-1/ by Coordinates of M in the ordered basis B it the coordinates of M in C is Mc = -3 is given by [M] := To [M].

. MR = |V3 -1 T-37 -514 - / 1-3 (3)(-3)+(-01-3) 45/4)(-3) + (-42)(-3) - - 1+3 [ 15/4+3/2 IMDB = 2114 c) Since [M] = (-3) (M] - [sic] Mc .. [M 16 = [c; C ₂1 37 = -30, -3C2 ..[M] 2 = -3 (cit.c.) 3 =-3 10- 1-5-1 2 =-3 (1-3 Otoll L-5-2 -13 =-31- 20 1-72