Q20Single correct3 Marks24 Dec 2023

Let V be a vector space and v1, v2, v3 be three distinct elements in V. If every v in V can be expressed as a unique linear combination of these three vectors, which of the following statements is true? Here, $\dim(V)$ refers to the dimension of V.

A

$\dim(V)$ = 3

B

We cannot comment on the exact value of $\dim(V)$. It lies in this range: 1 <= $\dim(V)$ <= 3

C

We cannot comment on the exact value of $\dim(V)$. It lies in this range: 0 <= $\dim(V)$ <= 3

D

We cannot pass any judgement whatsoever on the value of $\dim(V)$ with the given data.