# If homogeneous system the number of knowns then the system has

A. Only trivial solution

B. Trivial solution and infinitely many non-trivial solution

C. Only non-trivial solutions

D. No solution

Answer

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Hint: Use linear independence or dependence concept.

Since the system of equations is homogeneous so it’ll be consistent. It’s given to us that the number of known ones then one row is dependent on the other one. It means the system is not linear independent but linearly dependent. So, one or more vectors can be expressed as the linear combination of others. And hence it has infinitely many solutions including the trivial ones.

Note: The core of this problem is linear algebra. Try to understand the dimension of solution space and inherent linear dependency or independency concept.

Since the system of equations is homogeneous so it’ll be consistent. It’s given to us that the number of known ones then one row is dependent on the other one. It means the system is not linear independent but linearly dependent. So, one or more vectors can be expressed as the linear combination of others. And hence it has infinitely many solutions including the trivial ones.

Note: The core of this problem is linear algebra. Try to understand the dimension of solution space and inherent linear dependency or independency concept.

Last updated date: 24th Sep 2023

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