Math Is Fun Forum

Ah thanks Bob, I'll give it a try, it just seemed that using the a,b and c terms would be easier, I didn't think to let the the determinant = D, thanks!

Hi Bob,

Thanks, once again, for replying when I'm in need of help. I don't think I made my question clear, however - for which I do appologise. I was able to do those questions with a reasonable degree of ease, but, since they are 'show that' questions, I wanted to finish my answer with a mathematical conclusion. So, let's take my first question as an example, my approach was to find the determinant of the given matrix A, which, when evaluated came out to be abc-abc. What I then wanted to state is:

Therefore, for all values of a, b and c, the matrix A is singular.

Which, of course, follows from the result that the determinant is equal to abc-abc and is what the question had asked me to show.

However, I wished to state it in set builder notation.

My actual question, then, was about set-builder notation, I have a good idea of the workings of it, but expressions such as 'a, b and c are all elements of the set of real numbers' and quantifying over natural language sentences, as opposed to mathematical expressions are examples of things which I do not fully understand. So I was asking if anybody has any good articles or books on set builder notation (or even set theory in general) which I could have a look at, or has the time to give a quick tutorial in set-builder notation, such that I can fix problems similar to the ones above. These were merely examples of the kind of thing which I was struggling to express in set-builder notation.

Thanks

Merry Christmas

Ah, thanks bob, so it would seem that I did indeed make a mistake with the modulus signs - thanks!

Thanks Bobbym for the trouble. You are absolutely right, I've decided to move on. I have to say, I really don't think much of this textbook, but what can you do

Certainly, it is the newest edition of:

Edexcel AS and A Level Modular Mathematics FP1 (Further Pure Mathematics 1). This is the textbook accompanying the Advanced Level examinations set by the examining body Edexcel in Britain.

The ISBN number is: 978-0-435519-23-0 and is distributed by Heinemann.

See:

http://www.pearsonschoolsandfecolleges.co.uk/Secondary/Scotland/Maths/EdexcelModularMathematicsforASandALevel/ISBN/FurtherPureMathematics/EdexcelASandALevelModularMathematicsFurtherPureMathematics1.aspx (http://tinyurl.com/34dgwdm)

Hmmmm...That's interesting, but surely the area of a rectangle is given by the width multiplied by the height.

Hi Bobby

Thanks, 15 sounds like exactly the right answer, maybe I'm just tired and am doing something silly, but when I drew the rectangle I got a 5 x √10 rectangle. I assume it should be 5 x 3, but surely if the coordinates of our two points are (-1,0) and (0,-3) we need to do pythagoras, or have I constructed the rectangle incorrectly. It's entirely possible I have .

Hi Aartt, to truncate something is literally to shorten, or to cut off. So, if you truncate a decimal, e.g. 0.7456464, you simply shorten it, without regard to rounding, i.e. 0.745 would be a truncation of that decimal.

That's a very good point Bobbym, I completely overlooked that, for which I appologise.

Okay, well you will need that formula to answer my more advanced question. If you like we could discuss that now, however, I'm still perplexed by these questions. I can say with some degree of certainty that there are no values of x which satisfy those equations. In mathematics, that is a perfectly reasonable result, indeed it can be a useful result. Indeed in formal texts it would not be uncommon to see something like:

Obviously you don't need to worry about that, it just says there aren't any values of x which satisfy that equation, I just thought you might be interested to see how we can conclude that the our equation has no answers. However, having finally got to the point of my post, it's not very useful in teaching algebra to give students equations which have no solutions. Does the book have any answers, or does the question say, at any point, something like which of these equations can you solve for x? For those which can be solved, find x?