GATE 2004
December 8, 2024NTA UGC NET Aug 2024 Paper-2
December 8, 2024GATE 1996
| Question 7 |
Let Ax = b be a system of linear equations where A is an m × n matrix and b is a m × 1 column vector and X is a n × 1 column vector of unknowns. Which of the following is false?
| The system has a solution if and only if, both A and the augmented matrix [A b] have the same rank.
| |
| If m < n and b is the zero vector, then the system has infinitely many solutions. | |
| If m = n and b is non-zero vector, then the system has a unique solution. | |
| The system will have only a trivial solution when m = n, b is the zero vector and rank (A) = n. |
Question 7 Explanation:
→ It belongs to linear non-homogeneous equations. So by having m=n, we can’t say that it will have unique solution.
→ Solution can be depends on rank of matrix A and matrix [A B].
→ If rank[A] = rank[A B] then it can have solution otherwise no solution.
→ Solution can be depends on rank of matrix A and matrix [A B].
→ If rank[A] = rank[A B] then it can have solution otherwise no solution.
Correct Answer: C
Question 7 Explanation:
→ It belongs to linear non-homogeneous equations. So by having m=n, we can’t say that it will have unique solution.
→ Solution can be depends on rank of matrix A and matrix [A B].
→ If rank[A] = rank[A B] then it can have solution otherwise no solution.
→ Solution can be depends on rank of matrix A and matrix [A B].
→ If rank[A] = rank[A B] then it can have solution otherwise no solution.