GATE-2024-CS1(Forenoon)

Question 49

Let A be any nxm matrix, where m>n. Which of the following statements is/are TRUE about the system of linear equations Ax=0?

A	There exist at least m-n linearly independent solutions to this system
B	There exist m-n linearly independent vectors such that every solution is a linear combination of these vectors
C	There exists a non-zero solution in which at least m-n variables are 0
D	There exists a solution in which at least n variables are non-zero

Correct Answer: A