Computer Sciences > GATE 2024 SET-1 > Linear Algebra

Contributed by: Dr. Sarah Chen

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Let A be an n × m matrix with m > n. Which of the following statements is/are TRUE about the system Ax = 0?

A

There exist at least mn 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

Check Answer

Explanation

Correct : b,c

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