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SSC Pure Mathematics QUESTION #1287
Question 1
Which of the following sets forms a basis for \(\mathbb{R}^3\)?
  • {\((1,0,0),(0,1,0)\)}
  • {\((1,2,3),(2,4,6),(0,0,1)\)}
  • {\((1,0,0),(0,1,0),(0,0,1)\)}✔️
  • {\((1,1,1),(2,2,2),(3,3,3)\)}
Correct Answer Explanation
A basis for \(\mathbb{R}^3\) must have exactly 3 linearly independent vectors. Option (A): only 2 vectors. Option (B): \((2,4,6)=2(1,2,3)\) — dependent. Option (C): the standard basis — 3 independent vectors ✓. Option (D): all three are scalar multiples of \((1,1,1)\) — dependent.