Question

Determine all possibilities for the solution set of a homogeneous system that has y1 = 5, y2 = −3, y3 = 2 as a solution.

(a) one

(b) finitely many

(c) infinitely many

(d) either one or infinitely many

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Answer 1

The correct option is (c) infinitely many

Explanation: The possibilities for the solution set for any homogeneous system is either a unique solution or infinitely many solutions. Since the homogeneous system has the zero solution and y1 = 5, y2 = −3, y3 = 2 is another solution, it has at least two distinct solution. Thus the only possibility is infinitely many solutions.