Suppose that a homogeneous system of equations has basic solutions 1and 3 Let c be a real number. For which value of c is the column ( 1 2c c)' a solution to the homogeneous system? Justify your answer. If no such c exists, explain why.

(1 point) (Note: This problem has several parts. The latter parts will not appear until after the earlier parts are completed correctly.) Part 1 Solve the following system of linear equations: + 5y 5z 25 2x 11y 11z 55 - 3x 16y 16z 80 - 9y 9z 45 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: Part 2 Enter your solution below. If a variable is an arbitrary parameter in your solution, then set it equal to itself, e.g., w = w. X = y = Z = ... 出|田 +

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