Question

1) for R2 Given the vectors b1,b2, C1, and cz. B = {b1,b2} is a basis for R2C = {C1,C2} is a basis b = [i.bz = [33],4 = (-2) c2 = [4] (a) Find the change of coordinates matrix to convert from B to C. (b) Find the coordinate vectors [x]B, [x]c, lyle and [ylc given x = [11] y = [12]

Answer 1

3 b = (i), bz2), 92 (-2),(22(-) a biz ana + a2c2 (3) 2 0 (-2) + O2(-1) = at yar -201 Az U+Yaz 2 3 Caut yar) 0 → -20, - a 2 z 1 2 -Da-Yal=4 Adding and ③ we get -70, E7 a= -1 put art in o, we get -1 +4 0233 - 4 22 4 ar=1 so 3 & (?) = (-1) (-2) +49(-1) Có) "(-2) +*+1-4) (-24,- - (3) = 10,7 3 | Page - 3 dit 482 1-28,82 ritur -28 - r =6 s -ori-ur=24 Adding 6 and 6 wegel -78, = 21 TV2-3 put r=-3 in 0, weget

-3+ y 82 Z -3 482 8zzo 6 3 6 3 de @ (3)=63)(-a) + 10 () son from we get the change of matrix to convost from B toc is given by coordinabes - 3 0 :) b x = abitaba (-1)= a(?) + b -3 6 o -12 30-31 2 at6 b 2 3 at 10 b 2 3 1 (2 substrating Aedding @ ma weget o from @ weget 216 14 be 21 b 22 3 Ipage-2 ro usef 3 a = 1-6bz 1-6x2 1 - 4 a z E so, [x] 8 N 22/

(")= a(-2) + bc) fact - 6) (+1)= (a+46 3 at yb z-11 Melding a bel -oa ЧЬ Ч G & , weget -7 a=7 a=-1 wieget 1+ 4b =-11 Yb 2-10 from b2을 o 2 (2 こ (1) (2) - 2 / 2 (4) so, [x]c 2 (2) for Lalo (62)= a(?) +613) page-3 (52)= 3a - 31 12 3a - 3b a t 66 3a-3 b 2 12 a-b=4 a+bbiy - 2 substracting @ from, wegel 76=0 »[6z0 pub bro in enegee

Jazu 4 G) = 4(?) + 0 (3) []= (). For yo (12)- al )+b(1) 24 h atub 2 12 » -2a-b zu -oa-4b216 -e Aedding Band , weget - 7a2 20 Ta=-4 put azy in ①, weget -4 tub 2 12 0216 ТЪгч (%) 244) (-2)* *(-) page-y (yle Z