Question

(1 point) Which of the following sets of vectors are linearly independent? A. {( 10, -16), (-5, 8 )} B. {(-4, -7, 1, -8), (1, 3, 9, 7)} c.{(-2, -6)} D.{(1, 3), (-7, 1)} E.{(-9, 4), (0,0)} F.{(0,0)} G.{(-3, 7), (9,-4), (5,-8)} H.{(6, 1, -8), (1, 2, 5)}
please help thank you,

Answer 1

(-) { (10,-16), (-5, 8)] - {2 (5,-2), (-5, 8) } folom here that Just twice Linearly Dependent we See of 1st 2nd vectoll is Vectodt hence they are 2.) oll { (-4,-7, 1-8) (1,3,5,7) 3 let a, b be real, conostants then, at-4, 7, 1,-8) +6 (1,3, 9,7)=0 Eyath - 2a+36, athb, 84+76)=0 on equating -4q+6=0,-79+36=0 atab=0, 8atzb=a i DD liv - uath =0 X 3. /2a+36=0 - Tatab=0 -79 +36=0 + – 5q=0 Put in ' [b=0 » [a=o nowe, Hence, L'I. I linearly Independent).

-3 a tabt sc =0 Ta 46 -8c=0 Here, there alle 3 variables & only 2 equations in this lase always L.D. { (6.1,-8), (1,2,5)) 1h) 69th 0-1 a +2650-2) -Sat60-3) 6a+b=0 bo tzb=0 -1160 Tb=0 & Lazo Hence, L-1. 59 Sets L.I. 040 & {B, D, HI