INSTRUCTIONS:

1) Do all necessary steps

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

(2) Consider the following system of equations: -mitty = b1 (* ) -max + y = b2 (a) Prove that if my # me, then (*) has exactly one solution. What is it? (b) Suppose that my = me. Then under what conditions will (*) be consistent? (c) Restate the results of (a) and (b) in geometrical language.(3) Consider the following system of equations: ctytz=2 a + 3y + 32 =0 (# ) r+ 37+ 62 =3 (a) Use Gaussian elimination to put the augmented coefficient matrix into row echelon 1 1 1 a form. The result will be 01 1b where a = __ , b = _ , and c = 0 01 C (b) Use Gauss-Jordan reduction to put the augmented coefficient matrix in reduced row ood echelon form. The result will be 0 10 c where d = , and 0 1 f = (c) The solutions of (*) are c = _, /= - , and = = (4) Consider the following system of equations. 0.003000x + 59.14y = 59.17 5.291x - 6.130y = 46.78. (a) Using only row operation III and back substitution find the exact solution of the system. Answer: = = (b) Same as (a), but after performing each arithmetic operation round off your answer to four significant figures. Answer: =