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

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

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

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

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

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

Okay, thanks to both of you. Stupid book.

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

luca-deltodesco wrote:

Wait, have I done something wrong here?

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

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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