Question

Determine all possibilities for the solution set of the homogeneous system that has y1 = 6, y2 = −4, y3 = 0 as a solution.

(a) zero

(b) infinitely many

(c) finitely many

(d) only one

I have been asked this question in unit test.

This question is from Counting topic in chapter Counting of Discrete Mathematics

Answer 1

The correct option is (b) infinitely many

Explanation: Since m<n, the system is either inconsistent or has infinitely many solutions. Since y1 = 6, y2 = −4, y3 = 0 is a solution of the system, the system is not inconsistent. Thus the only possibility is infinitely many solutions.