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Let $J_{mtimes m} $ be the Jordan normal form with real $c$ on the diagonal and 1 on the super diagonal. Show that $$null (J-cI) subset null...
Asked on 02/12/2021 by Smirniy007
1 answer$$S(x) = frac{x^4}{3(0)!} + frac{x^5}{4(1)!}+frac{x^6}{5(2)!}+.....$$If the first term was $$x^3$$ and the next terms were $$x^{3+i}$$ then differentiating it would have given $$x^2.e^x$$ and then...
Asked on 02/12/2021 by Arko Chowdhury
4 answerConsider a random permutation of numbers $1,...,31415$. Let $A$ be the number of its fixed points (i.e. numbers which are not moved by permutation). Let $B$ be...
Asked on 02/12/2021 by AliBA
1 answerFind $a$, $b$ such that $x^2 - x -1$ is a factor of $ax^9 + bx^8 + 1$The second polynomial can be rewritten as$$ax^9...
Asked on 02/12/2021 by Aniruddha Deb
6 answerI am reading a proof for a theorem and in the proof we make use of a function $w_z(t)$ defined by the initial value problem $dw_z(t)/dt = -phi(w_z),...
Asked on 02/12/2021 by StannisBa
0 answerIn the following corollary to the inverse mapping theorem by Serge Lang, Fundamentals of Differential Geometry, 1999, p.17-18, there are two things in the proof which I don't understand, the...
Asked on 02/12/2021 by Roland Salz
1 answerHow many bracelets can be made with 5 beads in one colour and nine in the other (rotated and flipped bracelets are considered the same). I'm trying to use Burnside's...
Asked on 02/12/2021 by Patrycja
1 answerThe inequality is from "Introduction to algorithm" of CLRS, section 25.1. What I tried so far is to express $n-1 = e^{ln(n-1)}$; consider the case when $n-1 =...
Asked on 02/12/2021 by Hiep
1 answerThe problemI want to find a boolean function $f(x,y):{0,1}^n rightarrow {0,1}$, where $x={x_i}_{i=1}^{m}$ and $y={y_i}_{i=1}^{k}$ are $m$ and $k$ boolean variables, such that:$m,k ge...
Asked on 02/11/2021
1 answerShow that the curve $$ ay^{2}=x(x-a)(x-b) $$ has two and only two points of inflexion This is a question that I have stumbled upon while going through the book...
Asked on 02/11/2021 by theunixdisaster
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