Math Is Fun Forum

!nval!d_us3rnam3

Member

Registered: 2017-03-18

Posts: 46

Matrices problem

We're going to consider the matrix

(a) Let

.

Find the

such that

(b) Find a formula for

.

(You don't need to prove your answer, but explain how you found it.)

(c) Using parts (a) and (b), find a formula for

I haven't been able to get anywhere on this problem; an explained solution would be much appreciated. Thanks!

Last edited by !nval!d_us3rnam3 (2019-06-11 12:14:24)

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"If we wanna be great, we can't just sit on our hands" - 2017 NFL Bears draft

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Matrices problem

hi !nval!d_us3rnam3

I've inserted [math/math] tags to make your matrices appear properly.

If you find the inverse for P then you can do this:

That should get you started.  Post back D if you need more.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

!nval!d_us3rnam3

Member

Registered: 2017-03-18

Posts: 46

Re: Matrices problem

I found D to be

. Can you help me through parts B and C, though? This is due tomorrow, so I could use a detailed explanation.

Last edited by !nval!d_us3rnam3 (2019-06-12 08:08:02)

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"If we wanna be great, we can't just sit on our hands" - 2017 NFL Bears draft

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Matrices problem

hi !nval!d_us3rnam3

That's what I'm getting for D too.

Try working out D^2 and D^3.  You'll spot a clear pattern and shouldn't have difficulty 'guessing' what D^n would be.
Finally consider

(PDP -¹) (PDP -¹ ) (PDP -¹ ) (PDP -¹ )…. (PDP -¹ ) = P D (P -¹P) D  (P -¹P)  D  (P -¹P) D  (P -¹P)  D ….D P -¹ = P D^n  P -¹

Hope that helps,

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob