For what values of $ a $ is the set $A=\{(a^2,0,1),(0,a,2),(1,0,1)\}$ a basis of $\mathbb{R}^3$
52888
Find all values of a for which $\{v_1,v_2,v_3\}$ form a basis for ${\bf R}^3$
9700
Consider the subset $B=\{(x,y):x^2+y^2\leq 1\}\ \subseteq \mathbb{R}^2$. Show that $\vert B \vert = \vert \mathbb{R}^2 \vert$.
142315
How does the Axiom of Regularity apply to $A=\{1,2,3\}$?
86309
Whether the set $A$ is a compact subset of $M_3(\Bbb R)$.
151467
An infinite generating set of a finite dimensional vector space contains a basis
31710
Show that $\mathcal{J}=\{[a, a+1) \mid a \in \mathbb{R}\}$ generates the Borel set of $\mathbb{R}$
158364
Are there uncountably many $A\in M_3 (\mathbb {R})$ such that $A^8=I $?
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?
148876
What is the meaning of $\mathbf{Q}(\sqrt{2},\sqrt{3})$
57037
How does $(a,b)$ where $a,b\in \mathbb{Q}$ form a basis for $\mathbb{R}$?
114142
How to show that $\mathbb{R}^3$ is the direct sum of $W_1={\rm span}\{(1,1,1)\}$ and $W_2={\rm span}\{(1,0,0),(1,1,0)\}$?
147159
Determine the set of values of $\exp(1/z)$ for $0<|z|<r$
134999
Writing empty set as union of basis elements for a topology.
46622
Let $ Y = \{ (1,1),(0,0\} \subset \mathbb A_k^2$. Find the $ \mathbb I(Y)$.
145094
Is my basis for $U=\{p \in \mathcal P_4(\mathbb R) \mid p(6)=0\}$ correct?
138653
Is $\mathbb{R}$ a subspace of $\mathbb{R}^2$?
34714
What is the relationship between $\ker(A), \ker(A^2), \ldots, \ker(A^n)$?