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zetafunc.

Guest

Matrix Transformations... am I wrong?

From the FP1 Sample Assessment Materials...

"The rectangle R has vertices at the points (0, 0), (1, 0), (1, 2) and (0, 2).

(a) Find the coordinates of the vertices of the image of R under the transformation given
by the matrix A =

, where a is a constant."

I did this:

AR = R'

This is completely wrong according to the mark scheme. They apply the transformation R but to only 3 points and get a completely different answer.

Here's part (b).

"Find det(A), giving your answer in terms of A."

This is the only answer I can seem to get correct: det(A) = a + 4.

Part (c): "Given that the area of the image of R is 18, find the value of a."

Using "Area of image = Area of object * |detA|"...

18 = 2*(a+4)
9 = a + 4
a = 5

They get a = 3.

I don't know if it's errors or just me missing something stupid...

Please help me to see where my error is. Thanks.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Matrix Transformations... am I wrong?

Hi;

First thing your matrix multiplication is incorrect.

You do not need to include (0,0) because that point does not move under the translation. That might be why they only used 3.

I really do believe that a = 5, I have a nice plausibility argument. It is not too difficult to prove that 3 is wrong!

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc.

Guest

Re: Matrix Transformations... am I wrong?

Ah, how could I be so stupid! 4*2 is clearly not 6. Thanks for telling me! Was worried that maybe I was doing matrix multiplication wrong or something...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Matrix Transformations... am I wrong?

But that does not settle the question of what a equals. I can definitely prove it is not 3 and that one possible answer is 5. I can not prove that 5 is the only possible answer but I suspect that is true.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

zetafunc.

Guest

Re: Matrix Transformations... am I wrong?

But that does not settle the question of what a equals. I can definitely prove it is not 3 and that one possible answer is 5. I can not prove that 5 is the only possible answer but I suspect that is true.

These papers were made from a batch of papers titled "FP1 Practice Papers A-D" which are unofficial and not made by people who work for Edexcel. There are lots of errors in the papers (at least one question on each one I found was impossible). I think this might be one of them...

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Matrix Transformations... am I wrong?

Okay then, stick with the 5.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.