Question

17. The standard matrix of the the linear transformation that represents projection onto the vector 1 m onto the vector (9)}{-1 9 ®}1] (0}{-1) none of these [1 2 3] 18. The matrix O O 5 can be reduced (using elementary row operations) to [2 4 0 100] [120] 1 007 (A) 0 1 0 (B) 0 1 0 (0) 0 1 0 (D) none of these LO 0 1 LO 0 0 Lo o o 19. Which of the following is orthogonal to v = (D) none of these 20. Which of the following is pealed to v = 1) 20. Which of the following is parallel to v = 101 (A) (B) 6 2] (D) none of these -1| 5 ] [ [

Answer 1

let A-L] that Standard matrix of the linear Transformation represents projection onto the vector = À (ATA) WAT [!](6-0 []J11-13 FJ (0*(1-1) = ['JL)2-] * *[:30 -0 = 6., 7] so option © is true.

18 Sol lot mo l'oc II 2 37 lot Alo os amo si a 37 Rg Ry - 2R, on oop so Lo -6] si a 37 R2 1; R ; Rgs 1 R3 R - 3 R and R3 R₃-R2 = [1 2 of R lo 01 Lo o od so, a None of these <V, V₂> =0. for orthogonal So for option @ © So, <Y, Vz) = 4xl-1) +21–2)+(-2)(-4,) =~11~4 78=0 so it is orthogonal. <VVn) = 4(2) +211 +(-2)(-)) = 8 + 2 of 2 -12 to so it is not orthogonal

© Lvova) = 4191 +21-1)+1-23.00) - 8 -2 40 = 6 to so it is not orthogonal. . option is true. binen that - wc for per hava vectors to be paralld it must be of multiple of the given vector. so, lt v=173 ]=-1}] =24 e 5 i, option ® is true iela)
This is the required solution.