Michael Biro
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 Apr 18 awarded Yearling Apr 15 comment Volume of a pencil Your first equation is correct, but you haven't factored out the 2 properly in the second one. Apr 15 comment Volume of a pencil Substitute $110 - h$ for $x + y$ and manipulate. You know the equation you are trying to reach, so it shouldn't be too hard to get there. Apr 15 answered Volume of a pencil Apr 5 comment Notation — How do I denote the derivative of a reciprocal evaluated at some value? OK, so instead do $(\frac{1}{f})^\prime(0)$? Apr 5 comment Notation — How do I denote the derivative of a reciprocal evaluated at some value? How about $(f^{-1})^\prime(0)$? Apr 1 comment Is there a difference between $x=0$ and $0=x$ Equality is symmetric, so if $a = b$ then $b = a$. The statements are different, but logically equivalent. Mar 28 answered Linear Algebra Orthogonality Proof Mar 28 comment If the positive series $\sum a_n$ converges does $\sum a_n \log(a_n)$ converge? It still works as $\log \frac{1}{n \log^2 n} = - \log n - \log \log^2 n$ Mar 28 answered If the positive series $\sum a_n$ converges does $\sum a_n \log(a_n)$ converge? Mar 23 answered Partitioning the edges of $K_n$ into $\lfloor \frac n6 \rfloor$ planar subgraphs Mar 23 comment Finding if the orthonormal basis of P1 with a given inner product The zero vector can never be in a basis. Take $1,t$ and do Gram-Schmidt. Mar 20 comment Rudin 1.11 Lower Bounds Since the ordered set specified is $S$, the intention was "bounded below in $S$". Mar 20 comment Rudin 1.11 Lower Bounds In your example, $B$ is not bounded below in $S$. Mar 12 comment If $A,B\in M_2(\mathbb{R})$, show that $(AB-BA)(AB-BA)$ is a scalar matrix. Do you know the Cayley-Hamilton theorem? Mar 5 comment Do $A$ and $p(A)$ have the same eigenvectors? What if $c_i = 0$? Mar 5 comment Should I be concerned if I cannot solve most exercises in my textbook? I suppose it depends. How long are you trying problems before giving up? Do you feel like the proportion of problems you can solve without checking the solutions is increasing? etc... Feb 21 comment T/F: any number that can be written as a fraction is rational. What about $\frac{\sqrt{2}}{2}$? Feb 18 comment Given the determinant determine the value of the matrix What have you tried? What properties of determinants do you know? Feb 17 answered Show that $\binom{2n}{n}+\binom{2n}{ n-1} = {1\over2}\binom{2n+2}{n+1}$