INSTRUCTIONS:

1) Do all necessary steps

2) This is a whole paper. No data is missing.

(5) Find the values of & for which the system of equations (atky = 1 krty = 1 has (a) no solution. Answer: (b) exactly one solution. Answer: (c) infinitely many solutions. Answer: (d) When there is exactly one solution, it is r = and y = (6) Consider the following two systems of equations. atytz=6 x + 2y + 2= = 11 (1) 2x + 3y - 42 = 3 and at y+ z= 7 + + 20+ 28 = 10 (2) 2r + 3y - 4z = 3 Solve both systems simultaneously by applying Gauss-Jordan reduction to an appro- priate 3 x 5 matrix. (a) The resulting row echelon form of this 3 x 5 matrix is (b) The resulting reduced row echelon form is (c) The solution for (1) is (_ ) and the solution for (2) is (. (7) Consider the following system of equations: C - y- 32 = 3 + 2=0 20 + 7: = c (a) For what values of c does the system have a solution? Answer: c= (b) For the value of c you found in (a) describe the solution set geometrically as a subset of R&quot