INSTRUCTIONS:

1) Do all necessary steps

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

(9) Consider the following homogeneous system of linear equations (where a and b are nonzero constants). r + 2y =0 ar + By +32 = 0 by + 52 = 0 (a) Find a value for a which will make it necessary during Gaussian elimination to inter- change rows in the coefficient matrix. Answer: a = (b) Suppose that a does not have the value you found in part (a). Find a value for b so that the system has a nontrivial solution. Answer: b = $ + Sa where c = and d = (c) Suppose that a does not have the value you found in part (a) and that b = 100. Suppose further that a is chosen so that the solution to the system is not unique. The general solution to the system (in terms of the free variable) is ( 2 2, 2 where o = and 8 =