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#2 Re: Help Me ! » More Vectors and Matrices (urgent) » 2019-06-19 09:54:33

For part (a), what happens when you multiply that matrix by each of those vectors?

For part (b), you'll have been able to find some number
(called a 'scalar multiple') such that
, and likewise for the others. This then tells you that
. Use this to write down an expression for
and therefore
.

For part (c), trial and error is easiest here: try to find a way of making 10 from a linear combination of
and
. Then see if that same linear combination works for the other two vector components.

For part (d), you can use your linear combination found in part (c) to replace that vector with something that looks like
. You can then split the matrix multiplication into three parts: can you see how?

#4 Re: Help Me ! » Find A special offer price ? » 2019-05-25 23:17:03

Hi Lasson,

Can you please check your other percentages thread?

#5 Re: Help Me ! » Algebra 1 /Solve expression » 2019-05-25 06:12:58

Hi,

You might find this link useful:

#6 Re: Help Me ! » Find out the% » 2019-05-25 05:46:45

Hi Alexandr2,

I responded to your other post -- please have a look when you have time.

One of them secured 9 marks more than the other

OK: let's say that one student got
marks and the other student got
marks (that's 9 marks higher than the other student).

Then, the sum of their marks is
. Does that help?

Let me know if you get stuck.

#7 Re: Help Me ! » What percentage should be removed? » 2019-05-25 04:19:24

Hi Russia,

Have you considered registering an account with us? You can do this by .

The old price of the coat is $20, and the new price is $15. That means the price has reduced by $5 (since 20 - 15 = 5). So now you just need to find out how much percent $5 represents as a fraction of the old price. This is:

Please let us know if you need any further help!

#8 Re: Help Me ! » Vector problem, help ASAP » 2019-05-23 22:05:29

Part (b) is similar, but bear in mind that you have to prove both directions. First, let's see if we can do the reverse direction (not scalar multiples => any vector can be represented in the form
).

Suppose that instead of
and
you have
and
. In other words, instead of having

you have this instead:

Another way of writing this is:

Now, let's say you wanted to solve this system for
and
. You'd need to find the inverse of
, right? But for that inverse to exist, the determinant can't be equal to 0. In other words, for that thing to have a solution, you must have:

i.e.

which tells you that
isn't a multiple of
. Remember, saying that
and
are scalar multiples of each other just means that you can find some real number
such that
, or in other words:

i.e.

Now, for the forwards direction (any vector can be expressed as
=>
and
aren't multiples of each other), try proving the contrapositive, i.e. show that if
for some real number
, then not every vector can be expressed in the form
. Let me know if you have any more questions!

#9 Re: Help Me ! » Vector problem, help ASAP » 2019-05-21 22:32:32

No worries -- let's look at part (a) first.

!nval!d_us3rnam3 wrote:

(a) Show that any two-dimensional vector can be expressed in the form

where
and
are real numbers.

Okay, let's take any two-dimensional vector, say,
. We want to know: can we find real numbers
and
so that:

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.

#10 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?

#11 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.

#12 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.

#13 Re: This is Cool » Integral of 1/sqrt(1-x^2) » 2019-05-12 22:37:24

Anthony Lahmann wrote:

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:

#14 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!

#15 Re: Help Me ! » Probability » 2019-05-04 04:02:01

How many breakdowns occur in total?

#16 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?

#18 Re: Help Me ! » [ASK] How to Read A'? » 2019-03-25 22:02:39

Monox D. I-Fly wrote:

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!

#19 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).

John E. Littlewood wrote:

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.

#20 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!

#22 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:

#23 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. smile

#24 Re: Exercises » Integration » 2019-01-18 03:03:53

Set

then use the trig identity

#25 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?

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