Question

I need help with 1 and 2

Problem 1.3.6 Which among the following sets B = {P,Q,R} do span R3? For each of th is there more than one choice of scalars or is the choice unique? 0 0 10 , Q = -4 ,R = 0 13 0 P-09).-() - (DP- (1) 4 - (8) .R- (1)

Answer 1

• P= (9).9=6), R=(8) P - Consider ap+bQ & CR = 0 o, a (3) +- (3)=c(8)= (7) * 9)- (3) si ac0 16 o ora bao sso or, cao } } 5:48,, Rz is limearly independent fet with 3 elements.

Again dimension of IR² is 3. Any linearly independent set in IR² spam IR? - 1B = { P, Q, R } stams ir 2. p= ( ), 5= (8) R= 0) Consider ap+bq + c R = T + C oy, a + | (= 1:) + N | a + + c | =0 t a+C b+C =0 a+c =0 a=rc . berci het, cal ..a=-1; b=-1, cal No, pigs, R are not linearly telependent, so, 1B = {P, Q, R} does not. Skan IR?