Let S be a finite linearly independent set of vectors in V, and let T be a subset of S. Show that T is a linearly independent set of vectors in V.
2287
If a set is linearly independent, a finite subset of that set is also linearly independent
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
23095
Prove that T is a linear transformation
72391
linear dependence proof using subsets
132492
If a linear transformation $T$ has $z^n$ as the minimal polynomial, there is a vector $v$ such that $v, Tv,\dots, T^{n-1}v$ are linearly independent
94077
Proof of linear independence of $e^{at}$
147013
Subset of a finite set is finite
97049
If $v_1,...,v_m$ are linearly independent, then the span $v_1+w,...,v_m+w$ has dimension $\ge m-1$
107248
Prove that the set $ \{\sin(x),\cos(x),\sin(2x),\cos(2x)\}$ is linearly independent.
38516
Show a subset is subspace of a vectorspace and find the dimension
112231
Showing that a one-to-one linear transformation maps a linearly independent set onto a linearly independent set
53528
If $\ker f\subset \ker g$ where $f,g $ are non-zero linear functionals then show that $f=cg$ for some $c\in F$.
146664
The union of two linearly independent subsets
43871
Is this subset linearly independent or linearly dependent?
51313
Extension of linearly independent set to a basis in an infinite dimensional vector space
17087
Question concerning linear combinations of vectors and linear independence in Linear Algebra.
94929
Proof that the all bases of a subspace V consist of the same number of vectors?