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Noy's user avatar
Noy's user avatar
Noy
  • Member for 7 years
  • Last seen this week
  • Israel
4 votes
2 answers
930 views

Find the cardinality of the set of all equivalence relations in $\mathbb{R}$.

4 votes
1 answer
232 views

Finding a Jordan basis of a $3\times 3$ matrix

3 votes
3 answers
181 views

Find the determinant of the following $5\times 5$ real matrix:

3 votes
3 answers
483 views

Prove the function $f(x)= \begin{cases}x^2 & x\in\mathbb{Q}\\-x^2 & else\end{cases}$ is differentiable at $x=0$

3 votes
1 answer
241 views

Find a recurrence relation for the number of strings of length $n$ over $\{1,2,3,4,5\}$ such that :

3 votes
2 answers
173 views

The function $f(x)=$ ${b^mx^m}\over(1-bx)^{m+1}$ is a generating function of the sequence $\{a_n\}$. Find the coefficient of $x^n$

3 votes
0 answers
73 views

Let $B_1$ be some basis of $\mathbb{R^3}$ and $B_2$ be the ONB produced by $B_1$ after the Gram-schmidt process

2 votes
1 answer
486 views

Bijection from the set of all bases of the vector space $V$ (of dim $n$) to the set of all invertible matrices of order $n\times n$ such that:

2 votes
3 answers
656 views

Proving the equation $4x^3+6x^2+5x=-7$ has has only one solution using Rolle's or Lagrange's theorem

2 votes
1 answer
301 views

Recurrence relation and initial conditions for the number of ways to tile a road (of length $n$ cm) , using blue, red and green tiles such that:

2 votes
1 answer
112 views

Let $A$ be a finite set such that $|A|=n+1$ for some $2\le n$ and let $R\subseteq A\times A$ be some reflexive relation in $A$. Prove the following:

2 votes
2 answers
64 views

Let $A,B$ be some sets such that $|A|=a, |B|=b$. Prove $\binom{a}{b}=|P_b(A)|$ is a well defined expression.

2 votes
3 answers
84 views

Let $f(x)=\frac{\arctan(x)}{x}$. Let $F$ be the anti-derivative of $f$ in $\mathbb{R}$. Prove $F$ is not bounded above in $\mathbb{R}$.

2 votes
0 answers
60 views

Find the exact number of times $f(x)=\displaystyle\sum_{n\neq 0}\frac{1}{n^{4.01}}e^{inx}$ is continuously differentiable.

1 vote
3 answers
155 views

Simple two variable limit problem, find the limit, if exists, of $f(x,y)=x^2\sin(\frac{1}{xy}) $:

1 vote
1 answer
81 views

Calculating $\lim_{(\Delta x,\Delta y)\to(0,0)} \frac{\Delta x(\sin (\Delta y) -\Delta y)}{\sqrt{((\Delta x)^2+(\Delta y)^2})^3} $

1 vote
1 answer
146 views

Let $ A\in M_n(\mathbb{C}) $ be an invertible and non-diagonalizable matrix. Prove that for all $k\ge 1 \Rightarrow A^k$ is not diagonalizable.

1 vote
2 answers
77 views

Show that for all $m\ge 2$ there is some invertible, non-diagonalizable matrix $A\in M_2(\mathbb{R})$ s.t $A^m$ is diagonalizable.

1 vote
1 answer
85 views

Find the adjoint operator $T^*$ of $T:V\to V$ defined by $Tx=x-\frac{2<v,x>}{||v||^2}v$ for some fixed $v\in V$, where $V$ is under $\mathbb{R}$.

1 vote
2 answers
61 views

Check the convergence of $\sum\limits_{n=1}^\infty \int^r_0 \sin^n(x)\cos(x)\,\mathrm dx$ where $r>0$

1 vote
1 answer
540 views

Show that if $p(x)=a+bx+cx^2$ is a 2nd degree polynomial such that $p(1)=p(2)=p(3)=0$ then $p(x)=0$, using determinants.

1 vote
0 answers
54 views

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be a continuous, diffrentiable given function. Find $\int^b_af^{(3)}(x)\ f'(x)dx$

1 vote
2 answers
194 views

Find the number of ways to arrange the numbers $\{1,2,...,n\}$ in a row so that for all number $x$:

1 vote
1 answer
798 views

For all $n\in\mathbb{N}$, let $a_n$ denote the number of strings of length $n$ over $\{1,2,3,4\}$ such that:

1 vote
1 answer
212 views

How many trees are there on $\{1,2,...,n\}$ vertices, such that vertices 1,2 are adjacent (there exists an edge between them)?

1 vote
0 answers
84 views

Prove/disprove: If $f$ has an anti-derivative in $[a,b]$ then $\int_a^b f(x)dx$ exists and is finite

1 vote
6 answers
1k views

Prove the equation $\ln(x) = \frac1 {x-1}$ has exactly 2 real solutions.

1 vote
4 answers
2k views

Let $T:V\rightarrow V$ be a linear transformation such that $T^2=2T$

1 vote
1 answer
28 views

Assume $B=\{b_1,...,b_n\}$ is a basis of some vector space $V$ and let $C,D$ be other bases of $V$. $[b_i]_C=[b_i]_D \forall i \rightarrow C=D$?

1 vote
2 answers
217 views

Find a necessary and sufficient condition