Question

2. Consider the linear system -2.c + 3y + 2 = 5 4.c +9y-322 = 5 -2.c + 18y - 292 = 20 (a) Write down the augmented matrix of the linear system. (b) Find the reduced row-echelon form of your matrix from part (a). (c) Using your answer to part (b), write down the solution to the linear system. Clearly indicate which variable(s) (if any) you are using as a free variable(s).

Answer 1

r system - 22+ 3y +z = 5 404 g 4 - 32z=5 -20+ 184-292 = 20 het given tinear system written in matrix form . [A16] = - 23 115 1 4 9 -325 L-2 18 -29 1201 it is Augumented matrix to given linear Now we reduced row- echelon form of Augumented matrix - XR, -/ -1/2 1-5/ [AB] n o 15 -30 15 1 XR2 [-2 18 -29 20 system. giren Rz7 ZR1 + R₂ - To Lo 15 15 -30 -30 15 15 Lo 152-30 151 0 0 0 0

R, 2 R TRI 10-12-17 01- 21 Loo oloj The corresponding system of equation is 4 - 12 = -1 0 y-2z = 1 I since a gy corresponds to leading is in the Augumented matrix we call them leading Vanable. The non-leading Variable z ahre free Vanabled We assume that free Vañable [=s. from equation ② y-22=1 y a 25 = 1 y = 7+28. . and equation o OL - =1+25 2 System The genaral solution of given linear = 22 +15, y = 1+2s 1 Z=13 Hence Solve