Computer Sciences > GATE 2024 SET-1 > Linear Algebra
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

Correct : b,c

Similar Questions

Consider the systems, each consisting of m linear equations in n variables. I. If m < n, then all such systems have a solution II. If m > n, then none of thes...
#111 MCQ
Let A be an n x n matrix with real number entries, where n > 2. Let B be a matrix obtained by interchanging two rows of A. Which of the following statements is/...
#931 MSQ
Let det(A) and det(B) denote the determinants of the matrices A and B, respectively. Which one of the options given below is TRUE?
#955 MCQ

Related Topics

No tags found

Unique Visitor Count

Total Unique Visitors

Loading......

Question Options

Contributed by: