iv] Is the set of vectors 4 , _3 1 2 linearly independent? If not, enter a nonzero solution to the 3 4 2 equation 1 5 8 o: 4 + ,3 3 + "r 2 = [l _ 3 4 2 Otherwise enter the zero solution {i.e. [0, o ,01}. [rth] = E B iv) Is the set of vectors linearly independent? If not, enter a non-zero solution to the equation 5 8 4 + B -3 +y 2 =0 3 4 Otherwise enter the zero solution (i.e. [0 , 0, 0]). [a, B, y] = [0,0,0] XThe given set of vectors is Now let us assume + 8 2 = ( :) - 4 +5/ +8 8 - 0. 49 - 3p+ 28 = 0 (2 ) - 3x + 4 1 + 28 = 0 (3 ) Pubstract (3) from (2 ) , we get ( 4 x - 3 1 + 2 8 ) - ( - 39 + 4 p + 28 ) 20 on 79 - 7B = 0 on on 9 = 6 Substractrie (is From 4 times of (2), we get 9 ( 40 - 3p + 28 ) - (- 4 + 5 1 + 8 8 ) on, 179 - 176 = 0 6 1 9 - 6 20 on let ous consider . B = K ( say) Substituting ng a = p = k in (1) we get 7 - K + 5 K + 8 8 =0 on 8 8 + 4 k 20 on 88 = - 9K on 8 = - 5 Here, a = p = k and 8 =- zk so the set of vectors are not linearly independent : [x, B , 8] = 1, 1 - 4 27