Exercises for Section 13.1 Complete the computations in Exercises 14. In Exercises 17-22, A, B. and C denote ordered pairs; 0 is the pair (0,0); if A =(x,,y,), then A = 1. (l,2)+(3,7)= 2.(2,6)6(2,10)= _ ,_ , nd , ' w _ 3_ 3i\8 18 Let A= (21, 41 ) 4-A=(-21 1,-41 ) - LHS = At( - A ) = (2, , 41 ) + (-21,, -41 ) = ( 71 , - 2 1 , 1 - 91 ) = ( 01 0 ) 1 (1 1 0 = (0, 0 )7 = 0 = RHS . (n) Hence LHS = RHS E i.e | At ( - A ) = o Hence proved ( AtB ) + ( = At (B+ ( ) - ) Let ! A= " ( 2 rigi ) (8)1 B = (2/2, 42 ) ( = (713, 43 ) 7. LMS = ( At B ) + ( = (71,4, ) + ( 2121 42) ) + ( 73143 ) = ( 2, +72 , Hit 42 ) + (13, 43 ) = (21, , y, )+ ( it /3 , 42 + 43,) = ( 2,, 41 ) + ( ( 72,42 ) + ( 23: 83 ) ) U= At ( B+ ( ) = RHS Henic LMS = RHS i.e ( AtB ) + ( =) At ( B+ ( ) Hence proved . CS Scanned with CamScanner820 At B = B+ A Let A = ( 21,,4 1 ) B = (M2 1 42 ) - LMS = At B = (71, 41 ) + (212, 42 ) ( z R t lp ( z xt c ) = commutative = (212 + 21, ] yz + 4 1 ) property in addition = (712 1 4 2 ) 7. (2 1 7 37 ) = B+A = RMS Hence LHS = RHS i.e AtB = BTA Hence proved. CS Scanned with CamScanner