Question
A is a 3 × 5 real matrix of rank 2. For the set of homogeneous equations Ax = 0, where 0 is a zero vector and x is a vector of unknown variables, which of the following is/are true?
Options :
The given set of equations will have a unique solution.
The given set of equations will be satisfied by a zero vector of appropriate size.
The given set of equations will have infinitely many solutions.
The given set of equations will have many but a finite number of solutions
Answer :
The given set of equations will be satisfied by a zero vector of appropriate size.
The given set of equations will have infinitely many solutions.
Solution :
Matrix = [A]3 × 5
Rank of matrix ρ(A) = 2
number of unknown variable, n = 5
Since, ρ(A) < n
The given equation will have infinitely many solutions including a zero vector of appropriate value.
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