Prove that, if $\{u,v,w\}$ is a basis for a vector space $V$, then so is $\{u+v, v+w, u+v+w\}$.
95206
If $\{u,v,w\}$ is a basis for $V$, then $\{u+v+w,v+w,w\}$ is also a basis: is this proof correct?
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.
113326
Proving orthogonality of vectors in a complex vector space
57609
Hahn-Banach proof by extension of basis
47015
Vector Space Structures over ($\mathbb{R}$,+)
151467
An infinite generating set of a finite dimensional vector space contains a basis
4240
The proof of Triple Vector Products
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
86034
Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$?
89058
Question on finite Vector Spaces, injective, surjective and if $V$ is not finite
61539
proof for a basis in $L^2$
61604
$V = V_1 + V_2$ confusion? Why is my "proof "incorrect?
52596
A basis for $k(X)$ regarded as a vector space over $k$
92510
Proving a vector space is infinite-dimensional
116823
VERIFYING: Proving an $n \times n$ Matrix Vector Space
151038
How to prove (A v B), (A → C), (B → D) therefore (C v D)
131132
Proofs using vector properties