GATE ECE 2020 | Question: 1

Question

If $v_{1},v_{2}, \dots ,v_{6}$ are six vectors in $\mathbb{R}^{4}$ , which one of the following statements is $\text{FALSE}$?

• A. It is not necessary that these vectors span $\mathbb{R}^{4}$.
• B. These vectors are not linearly independent.
• C. Any four of these vectors form a basis for $\mathbb{R}^{4}$.
• D. If $\left \{ v_{1},v_{3},v_{5},v_{6} \right\}$ spans $\mathbb{R}^{4}$ , then it forms a basis for $\mathbb{R}^{4}$.