Which of the following statements is/are true:

I. A X = 0, always have a solution.

II. It is not necessary that  A X = 0, will always have a solution.

  1. Only I
  2. Only II
  3. Both I and II
  4. Neither I and II

Answer (Detailed Solution Below)

Option 1 : Only I
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NDA 01/2025: English Subject Test
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Detailed Solution

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Concept:

The system of equations A X = 0 is said to be homogenous system of equations, then

If |A| ≠ 0, then its solution X = 0, is called trivial solution.

If |A| = 0. Then A X = 0 has a non-trivial solution which means the system will have infinitely many solutions.

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