Question

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : Set $\{(1,0,0), (0,1,0), (0,0,1)\}$ forms a basis of $V_3(\mathbb{R})$. Reason R : Let $V$ be a vector space over a field $F$ and $S$ be a non-empty subset of $V$, then $S$ is a basis of $V$ if
(i) $S$ is linearly dependent
(ii) $\text{span}(S) = V$. In the light of the above statements, choose the correct answer from the options given below

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true but R is NOT the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Hint:

Read assertion-reason questions carefully! A single incorrect word like "dependent" instead of "independent" makes a mathematical reason completely false.

Answer 1

The Correct Option is C