Math Is Fun Forum

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)

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)

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Matrices

Wait, have I done something wrong here?

?

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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.

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luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: Matrices

ah ok then I thought i was going crazy

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Daniel123

Member

Registered: 2007-05-23

Posts: 663

Re: Matrices

Okay, thanks to both of you. Stupid book.

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: Matrices

Wait, have I done something wrong here?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Matrices

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

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