Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**!nval!d_us3rnam3****Member**- Registered: 2017-03-18
- Posts: 46

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)*

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,541

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

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 Bundy

Offline

**!nval!d_us3rnam3****Member**- Registered: 2017-03-18
- Posts: 46

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)*

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

Offline

**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,541

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

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 Bundy

Offline

Pages: **1**