query: Let $U =\{ p\in \mathbb{P_4}(\mathbb{R}): p(6) = 0 \}$. Find a Basis of $U$.
positive_passages.docid: 145094
positive_passages.text: Is my basis for $U=\{p \in \mathcal P_4(\mathbb R) \mid p(6)=0\}$ correct?
negative_passages.docid: 154724
negative_passages.text: Every vector space has a basis
negative_passages.docid: 95206
negative_passages.text: If $\{u,v,w\}$ is a basis for $V$, then $\{u+v+w,v+w,w\}$ is also a basis: is this proof correct?
negative_passages.docid: 91500
negative_passages.text: Let $U, V \sim U(0,1)$ be independent. What is $P(U \leq V)$?
negative_passages.docid: 46821
negative_passages.text: Finding roots in $\mathbb{Z}_p$
negative_passages.docid: 9143
negative_passages.text: Solve $u_{xx}-3u_{xt}-4u_{tt}=0$ where $u(x,0)=x^2$ and $u_t(x,0)=e^x$
negative_passages.docid: 158156
negative_passages.text: Finding the dual basis for the space of polynomials of degree $\leq$ 2
negative_passages.docid: 75429
negative_passages.text: A Hamel basis for $\ell^p$?
negative_passages.docid: 34693
negative_passages.text: Prove $E^{\mathbb Q}[Y]=E^{\mathbb P}[XY]$ if $E^{\mathbb P}[X]=\mathbb P(X>0)=1$ and $ \mathbb Q(A)=E^{\mathbb Q}[X1_A] $
negative_passages.docid: 66892
negative_passages.text: Finding $P$ in $A = P^{-1}JP$ (Jordan Form)
negative_passages.docid: 152742
negative_passages.text: Finding a basis of an infinite-dimensional vector space?
negative_passages.docid: 106033
negative_passages.text: Solve the system in $\mathbb{R}$
negative_passages.docid: 156761
negative_passages.text: If $p+q+r=0$, find the value of the determinant
negative_passages.docid: 120766
negative_passages.text: Prove ${y_n}$ is a basis for a Hilbert space $H$.
negative_passages.docid: 37953
negative_passages.text: Primary Decomposition of $\mathbb{R^n}$ under T
negative_passages.docid: 52596
negative_passages.text: A basis for $k(X)$ regarded as a vector space over $k$
negative_passages.docid: 3846
negative_passages.text: Let $v_{1}=(1,-2,3),v_{2}=(0,-1,2)$. Enlarge $\{v_{1},v_{2}\}$ to a basis for $\mathbb{R}^3$.