Teaching CSIR NET Mock Test Series Engineering Mathematics Linear Algebra Eigenvalues

Let T : ℝn → ℝn be a linear transformation, where n ≥ 2. For k ≤ n, let E = {v1, v2...vk} ⊆ ℝn and F = {Tv1, Tv2...Tvk}. Then

1
If E is linearly independent, then F is linearly independent
2
If F is linearly independent, then E is linearly independent
3
If E is linearly independent, then F is linearly dependent
4
If F is linearly independent, then E is linearly dependent
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