In the homogeneous system ρ(A)< the number of unknowns then the system has
A
Only trivial solution
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B
Trivial solution and infinitely many non-trivial solutions
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C
Only non-trivial solutions
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D
No solution
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Solution
The correct option is D Trivial solution and infinitely many non-trivial solutions Since the system of equations is consistent and it is a homogeneous equation, hence trivial solution exists.
Since ρ(A)< number of unknowns, there are infinitely many non-trivial solutions to this system of equations.