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• March 28th, 2020, 16:11
Welcome to the forum! I guess that "between" is supposed to mean "among", but I am not sure about "even". If it means "at least", then the...
2 replies | 209 view(s)
• March 27th, 2020, 23:42
Here is this week's POTW: ----- Find the minimum value of $(u-v)^2+\left(\sqrt{2-u^2}-\dfrac{9}{v}\right)^2$ for $0<u<\sqrt{2}$ and $v>0$. ...
0 replies | 82 view(s)
• March 27th, 2020, 23:38
Hi MHB! I have decided to extend the deadline by another week so that our members can give this problem another shot and I am looking forward to...
1 replies | 202 view(s)
• March 26th, 2020, 14:09
Nice... (Smirk) Thank you very much!!! (Blush)
12 replies | 327 view(s)
• March 25th, 2020, 20:13
I've been using Sage for generating problems in linear algebra and graph theory. It has nice functions for generating random matrices with integer...
1 replies | 74 view(s)
• March 25th, 2020, 17:24
Yes, it does... (Nod) So is this sufficient to say that since it has to hold for every $\lambda$, it has to hold that $a_{12}=a_{22}=0$ and so the...
12 replies | 327 view(s)
• March 25th, 2020, 15:43
Oh sorry... We get that $3 \cdot x_1+ 0 \cdot x_2=3 \Rightarrow x_1=1$, and $x_2$ is arbitrary, so it is indeed a solution... (Wasntme)
12 replies | 327 view(s)
• March 25th, 2020, 15:36
This is wrong, since we would have the following: \begin{bmatrix} 1 & 0\\ 3 & 0 \end{bmatrix} \begin{bmatrix} x_{1} \\ x_{2}...
12 replies | 327 view(s)
• March 25th, 2020, 14:24
So whichever value $\lambda$ has, we should get the same matrix $A$. This is only possible when $a_{12}=a_{22}=0$. Thus, $A=\begin{bmatrix} 1... 12 replies | 327 view(s) • March 25th, 2020, 14:08 Oh yes, right... (Thinking) Even if we pick, for example,$\lambda=0$, we do not get a specific matrix$A$. How can we get further information?... 12 replies | 327 view(s) • March 24th, 2020, 14:52 Hello!!! (Wave) The general solution of the system$Ax=\begin{bmatrix} 1\\ 3 \end{bmatrix}$is$x=\begin{bmatrix} 1\\ 0 \end{bmatrix}+...
12 replies | 327 view(s)
• March 20th, 2020, 02:18
Here is this week's POTW: ----- Show that the set of real numbers $x$ which satisfy the inequality \sum_{k=1}^{70}\dfrac{k}{x-k}\ge...
1 replies | 202 view(s)
• March 20th, 2020, 02:15
Congratulations to the following members for their correct solution! 1. castor28 2. lfdahl 3. kaliprasad 4. Oxide Solution from Oxide: ...
1 replies | 231 view(s)
• March 19th, 2020, 08:52
Just as a heads up, when we make the switch over to XenForo I will need to close MHB temporarily to do this. I hope it won't take more than part of a...
10 replies | 2088 view(s)
• March 15th, 2020, 17:13
Yes, your suggestion is correct. We need to show that $x\in \bar{A}=A\cup(\bar{A}-A)$ implies $x\in A\cup\partial A$. This requires considering...
2 replies | 157 view(s)
• March 14th, 2020, 11:03
Hi all, I know it's been a series of "we're getting close" but the dev team I hired to help with the key pieces of functionality I listed above...
10 replies | 2088 view(s)
• March 13th, 2020, 10:03
Here is this week's POTW: ----- How many perfect squares are divisors of the product $1!\cdot 2! \cdot 3! \cdots 9!$? ----- Remember to...
1 replies | 231 view(s)
• March 13th, 2020, 09:58
Congratulations to the following members for their correct solution!(Cool) 1. castor28 2. kaliprasad 3. lfdahl Solution from castor28: The...
1 replies | 271 view(s)
• March 4th, 2020, 09:34
Here is this week's POTW: ----- Consider the sequence of numbers 4, 7, 1, 8, 9, 7, 6, ... For $n>2$, the $n$th term of the sequence is the...
1 replies | 271 view(s)
• March 4th, 2020, 09:31
Congratulations to the following members for their correct solution! 1. castor28 2. MegaMoh Solution from castor28: If the generic point of...
1 replies | 396 view(s)
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