Question

(1 point) (Note: This problem has several parts. The latter parts will not appear until after the earlier parts are completed correctly.) Solve the following system of linear equations: 12x 33y - 3z12 Which one of the following statements best describes your solution: A. There is no solution. B. There is a unique solution. C. There are 3 solutions. D. There are infinitely many solutions with one arbitrary parameter. E. There are infinitely many solutions with two arbitrary parameters. F. There are infinitely many solutions with three arbitrary parameters. Statement: b EEl Enter your solution below. If a variable is an arbitrary parameter in your solution, the set it equal to itself,eg. u-u.

Answer 1

x + 2 y - 2 z = -5 -x - y + 4 z = 12 12 x + 33 y - 3z = 12 write it in matrix form [1 -1 12 2 -1 33 -2 4 -3 -5 12 12] R_2 rightarrow R_2 + R_1 and R_3 rightarrow R_3 - 12 R_1 [1 0 0 2 1 9 -2 2 21 -5 7 72] R_1 rightarrow R_1 - 2 R_2, R_3 rightarrow R_3 - 9 R_2 [1 0 0 0 1 0 -6 2 3 -19 7 9] R_3 rightarrow R_3/3 [1 0 0 0 1 0 -6 2 1 -19 7 3] r_1 rightarrow R_1 + 6 R_3, R_2 rightarrow R_2 - 2 R_3 [1 0 0 0 1 0 0 0 1 -1 1 3] So, x = -1 y = 1 z = 3