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#151 Re: Help Me ! » Vector problem, help ASAP » 2019-05-21 22:32:32
No worries -- let's look at part (a) first.
(a) Show that any two-dimensional vector can be expressed in the form
where and are real numbers.
If we 'multiply out' the left-hand side, we get:
Now, we can add two vectors just by adding the matching components, so that:
In other words, we want to find real numbers and so that:which is exactly the same as solving the pair of simultaneous equations:
Remember, we're solving for and here. (Just pretend that and are any old real numbers.)Let me know if this makes sense -- happy to explain anything further if you need more help.
#152 Re: Help Me ! » Vector problem, help ASAP » 2019-05-21 06:54:16
Hi !nval!d_us3rnam3,
Thanks for your post -- I fixed your LaTeX.
For part (a), suppose you've got some vector in . Then, you've just got to solve this pair of simultaneous equations for and :Does that make sense? (Let me know if anything sounds confusing -- happy to help.)
For part (b), suppose that instead of and you have and . This gives you the system:What sorts of conditions do you need here for that to have a solution?
#153 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-15 04:20:32
Thanks phrontister, that work pretty well. Hard to believe it has been two whole years.
#154 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-13 09:16:45
There is, however, still one issue: I can't view bobbym's post history, probably due to his post-count being so high. I'm probably not alone in saying that I miss him very much, and his insightful posts were a joy to read. It would be nice to be able to see some of his final messages again, before he left us.
#155 Re: This is Cool » Integral of 1/sqrt(1-x^2) » 2019-05-12 22:37:24
I will integrate 1/sqrt(1-x^2) by u-substitution. Here's how I did it:
After we did the u-substitution, we end up with the exact same integral, but with a negative in the front. What happened?
Your issue is here:
The correct implication is:
#156 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-05-09 21:07:18
The new update has been great so far. Deleting posts happens more or less instantaneously now, as opposed to having to wait a few minutes. No problems yet!
#157 Re: Help Me ! » Probability » 2019-05-04 04:02:01
How many breakdowns occur in total?
#158 Re: Help Me ! » Probability » 2019-04-28 21:10:36
For part b, calculate how many breakdowns occur in total. How can you use this to calculate, say, the probability that no breakdowns occur?
#159 Re: Maths Is Fun - Suggestions and Comments » Minor Upgrade - may or may not go smoothly » 2019-04-16 02:51:46
Fingers crossed!
#160 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-25 22:02:39
And here I thought that A' in the context of sets meant the complement of A.
It can indeed -- the notation can be quite varied!
#161 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-24 21:51:02
A' is read as 'A dash' in British English and 'A prime' in American English, although at my university 'A prime' was far more common, probably due to American influence.
In Littlewood's Miscellany, Littlewood jokes about this notation used in the context of sets (in point-set topology, A' is the set of all limit points of A, so that A' is called the derived set of A).
I have had occasion to read aloud the phrase "where E' is any dashed (i.e. derived) set". It is necessary to place the stress with care.
#162 Re: Exercises » Number of integer solutions » 2019-02-24 05:31:26
Hi Amartyanil,
Yes: try looking at that equation modulo 2 and modulo 3. From there you can deduce that x is a multiple of 2 and that y is a multiple of 3, which allows you to reduce that equation into something much simpler!
#163 Re: Introductions » Kamov's introducing himself » 2019-01-27 00:07:06
Welcome to the forum, Kamov!
#164 Re: Help Me ! » Integration » 2019-01-26 06:28:43
Hi Math 1122,
Welcome! Why not register an account with us?
You can start by using the identity
You'll also need (some, if not all of) these facts:
#165 Re: Exercises » Integration » 2019-01-25 11:16:35
Hi Bob,
I made a video explanation here, if Zeeshan 01 would like to have a look. 
#166 Re: Exercises » Integration » 2019-01-18 03:03:53
then use the trig identity
#167 Re: Help Me ! » Express ∛(7 + 5√2) in the form x + y√2 » 2019-01-10 07:39:45
Hi segfault,
Welcome to the forum!
Suppose that there are some values x and y for which ∛(7 + 5√2) = x + y√2. What happens if you cube both sides of that equation?
#168 Re: Maths Is Fun - Suggestions and Comments » Happy New Year, 2019! » 2019-01-04 10:32:09
Happy New Year!
#169 Re: Maths Is Fun - Suggestions and Comments » Merry Christmas! » 2018-12-24 23:43:29
Merry Christmas!
#170 Re: Exercises » Formula » 2018-11-29 03:12:42
#171 Re: Help Me ! » Number Properties » 2018-11-15 22:26:31
#172 Re: Help Me ! » Quasilinear 2nd order PDEs with inital data » 2018-10-29 22:32:14
Hi Emma22,
Welcome to the forum. Have you considered registering an account with us?
The general solution obtained is u(x,t) =F(x^2-t^2*exp(u)) and the initial condition is u(x,0)=2ln(x)
#173 Re: This is Cool » Repeated cosine converges! » 2018-10-10 01:34:18
Hi Βεν,
Nice contribution! Yes, the repeated iteration of the cosine function converges: actually, it converges to the fixed point of the cosine function, i.e. the solution to . (I think the two different answers come from using degrees versus radians rather than real vs imaginary.) There are ways of calculating this in terms of the Lambert W function or some nice infinite sums of Bessel functions I think.You can prove that a solution to the above equation exists via Brouwer's fixed point theorem (and probably the contraction mapping theorem too).
#174 Re: Introductions » Who am I,Βεν Γ. Κυθισ? » 2018-10-10 00:46:17
Hi Benjamin,
Welcome to the forum!
#175 Re: This is Cool » Something ineteresting » 2018-10-10 00:33:14
it should be (a^m)n^a.