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## #1 2009-03-24 08:29:40

Daniel123
Member
Registered: 2007-05-23
Posts: 663

### Matrices

It's given that:

a) Show that

, and hence find
.

b) The matrix C satisfies the equation

. Find p, q, r such that the image of
under the transformation represented by
is

I've done the first bit, and got

, which I know is correct.

For the second part, the quickest way I can think to do it is to find (B+I)^2 - BI, then find its inverse and postmultiply by (p,q,r). Is this the best way?

Thanks.

EDIT: Actually, using my above method, I end up with

, which would imply that
doesn't exist?

Last edited by Daniel123 (2009-03-24 08:35:58)

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## #2 2009-03-24 08:54:46

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Matrices

which does infact give it's determinent as 0.

hmmm

Last edited by luca-deltodesco (2009-03-24 08:58:56)

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #3 2009-03-24 09:14:25

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Matrices

Wait, have I done something wrong here?

?

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #4 2009-03-24 09:41:51

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Matrices

I get that det(B) = 1.

det(BC) = det(B)*det(C) = 0
⇒ det(C) = 0
⇒ C^-1 doesn't exist.

So the jump from line 3 to line 4 doesn't work.

Why did the vector cross the road?
It wanted to be normal.

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## #5 2009-03-24 09:44:14

luca-deltodesco
Member
Registered: 2006-05-05
Posts: 1,470

### Re: Matrices

ah ok then I thought i was going crazy

The Beginning Of All Things To End.
The End Of All Things To Come.

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## #6 2009-03-24 11:10:14

Daniel123
Member
Registered: 2007-05-23
Posts: 663

### Re: Matrices

Okay, thanks to both of you. Stupid book.

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## #7 2009-03-24 11:19:46

JaneFairfax
Member
Registered: 2007-02-23
Posts: 6,868

### Re: Matrices

luca-deltodesco wrote:

Wait, have I done something wrong here?

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## #8 2009-03-24 11:53:59

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

### Re: Matrices

True, but then you get to luca's by using I=B^3.

Why did the vector cross the road?
It wanted to be normal.

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