Given $a_1,\dots ,a_n\in V$, the set $W$ of all linear combinations of $a_1,\dots ,a_n$ is a subspace of $V$.
94405
Let $W$ be the set of all linear combinations of $v_1,...,v_n$. Then $W$ is a subspace of $V$.
72551
Proof that $\rho = \pm1$ implies linear combination
67191
When is the union of a family of subspaces of a vector space also a subspace?
102458
Subspace generated by permutations of a vector in a vector space
62065
Prove that $v_1, \dots v_n$ is a basis of V.
35625
Direct sum of orthogonal subspaces
106756
Union and Intersection of Sets $A_{i}$ and $B_{j}$
63260
Matrices whose Linear Combinations are All Singular
155999
How to prove the following properties of infimum and supremum involving the union and intersection of the sets $A_k$
124786
Prove that V contains a subspace of each dimension
4319
Vector space can be written as direct sum of subspaces
98949
Subspaces and annihilators
91087
For which values $r, s \in \mathbb R$ is the set $\{u, v, w\}$ linearly independent?
139951
Direct Sum of vector subspaces
86749
Prove that any set of vectors $S \subset \mathbb{R}^n$ containing the zero vector cannot be linearly independent
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
141794
Invariant subspaces of specific dimension