Teaching CSIR NET Mock Test Series Mathematical Science Linear Algebra Linear Dependence, Basis & Dimension
Which of the following is/are not true?
1
{(x1, x2) ∈ ℝ2 | x1 < x2} is a subspace of ℝ2 .
2
if {a1, a2, a3} is a basis for ℝ3 and b is a non-zero vector in ℝ3 then {b + a1, a2, a3} is also a basis of ℝ3.
3
If {x1, ... ... xr} is a linearly dependent set of vectors in ℝn then r < n.
4
If {x1, ... ... xr} is a spanning set for ℝn then r ≥ n.