Question

(1 point) For the following system to be consistent, –5x– 7y=5z = 5 17x-49y+kz =-10 –8x+ 7y+5z = 6 we must have, k =

Answer 1

«»;; ;; ܕܕܐ ܙ'; ܢ ܟܐ -5x - 74 - 5z = 5 17*-499 +K7 = -10 -82 +7y +52 = 6 we have to find ka? for which the above system in matrix form we have 1-5 -7 - 57a7 157 117 -49 K | ! is consistent ] [ ] -8 3 A x = 6 This is consistent ie have somtion Of Rank (A) = Rank (A:b) [4:57 - 1-5 -7 -5 1 57 17 -49 * | -10 1 -8 7 5 6 ] we to reduce it into Echelon form determine the value K - Apply R2 = R₂ + 12 R, ( -5 -7 -5 10 -36475 K-17 | 7 | -8 7 5 Apply R = K2 - зR, 1-5 -7 -5 c -364/5 y/S K-177 lo K 916 13 1-2) Apply R₂ = R3 + + R2

1-5 -7 - 5 -36476 K-17 7 TO +35 ! ! So for this to be consistent we must have K²-35 Otherwise of K=-35 we get 1-5 -7. -s 157 lo -364/5 -52 | 71 Here Rank (A) = 2 and Rank (A:b) = 3 7 Rank (A) & Rank (A: b) le system is in consistent of k=-35 - K7-35 for system to be consistent Thank you!