Question

Problem 5. (20) Find conditions(s) on bi, bz and by in order to guarantee that the linear system 13 consistent *+y-2=b 2x - 4y + 5z = b2 4x - 2y + 3z = b3 Solution. We use the augmented matrix and reduce the system. 11 1 -16] [1 1 -1 12 4 5 6 S-2R; + R2 R O -6 7 -4R1 + Rs R$ LA -2 3 6] LO - 6 7 11 -1 1 - R₂ + Rs → Rs 10 6 7 261 + b O 0 0 -25- 62 +63] bil -2b + b2 -45+ by Therefore any b2 that satisfies - 25 - by + b =0 makes the system consident,

I Undertand how the first two rows came about in the matirx, but I dont underatnd how the last row was calculated. How did it go from -4b1 +b3 to -2b1-b2+b3

Answer 1

Problem 5. (20) Find conditions (s) on b,ba and by in order to guarantee that the lincar system is consistent z+y-z=b 2r-4y+5b 4z-2y3:b Solution. We use the augmented matriz and reduce the system. Г1 1 -1 b1 -1 1 1 (-2R, + R, R -4R,+ RsR -2b, +b 0 7 -6 2 5 by -4 -4b,+ b 0-6 by 4 -2 3 1 by -1 -2b,+b 0 7 -R3 + RsR, -6 -2b, -b+b 0 0 0 Therefore any bthat satisfies-2b,-b+bs 0 makes the system consigent subitract -R2R3Rs we means amd 2nd Pul the bow Ro w hird hesulk how in thind R2 - 2b) t b2 - 6 -4b b3 - 6 R 3- 2=0 -4b b3 7 - 6 So -o - 2 b - 6 b2 7 --), 64bb24r) 0 0 C -2 b -b2t b3 о