Allied & ICAR Exam Bank • ALLIED_0017 MCQ • 1 Mark

Section 1: Engineering Mathematics

Linear Algebra

Subtopic: Solutions of linear equations

Question Statement:

If $A x = 0$ is a homogeneous system of 4 equations in 5 unknowns, the system has:

Options:

  • (A) Infinitely many non-trivial solutions
  • (B) Only the trivial zero solution
  • (C) No solution
  • (D) Exactly four solutions

Answer Key:

A

Step-by-Step Solution & Explanation

With 5 variables and rank $\le 4$, there is at least one free parameter, yielding infinitely many non-trivial solutions.
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