Question

(5 points) The following augmented matrix is in reduced row echelon form. Decode from the matrix the solution of the corresponding system of linear equations (using the variables X1, X2, and x3) or state that the system is inconsistent. (if a free variable is needed use the parameter t.) 1 0 3121 0 1 53 Lo 0 olo) con (10 points) Use row operations to compute the inverse of the matrix A = [ 53 -2] and use it to solve the system AX = B given by -2x+ 3y 10 5x + 8y = 20 Show all work!

Answer 1

Ganen Augmented mapie is (amin) - 13:30 write kn matora form Axzb. 3 1 D1 5 22 JI ро o 2₂ t 5z = 3. 22 = 3-5%. 2, +3715 = 2 x = 2-3X3 General solution is x 3 2-3x3 3-5x3 Xz 12 BJHE -3 : 52 Qa that Ginen 4- Now [??s] Form augmented makix. 160] E (1) - مام 8 R2+2 R2+ SR

17 als al sne -T:m«>R-30 2 0 16 0 - R, > R, (-2) 0 -8 1 1 :33] = [1 / A-'J ['s Hence, A - 2 NOU, A x = B Y=AB 5-3 10 -5- - 2 20 Х -50-60 -140 -50-40 [40] -90 140 C] -90