Matrices 2nd last question exam 2 WTF?

[tea.squaredd]

Ok, I lost 5 marks all on the linear module.
fuck, why walky talky when you're on a hike. Should be breathless.
argh stupid linear. can't believe i even lost those marks.

More OT, Yay! Matrices. Second last "During the 5th year" , last q. "400 juveniles and 0 adults" something like that

[Zykjeffery]

I wrote between 4th and 5th year   so is it right ??

[Deank]

Considering in the question it doesn't state when the female ducks lay the eggs, or what we're predicting, for example, the start of the year/end of the year, given that W₀ implies The very beginning, could you argue that you interpreted the question in a way that W₁ is the number of Ducks at the start of the year, given that the equation doesn't say other wise, resulting in The start of the 4th year being >half, and the start of the 5th year being <half, therefore during the 4th year is when the the colony will be halved..

[Natters]

the start of the year/end of the year
it did, start
i think it was in bold too >.<

[Deank]

the start of the year/end of the year
it did, start
i think it was in bold too >.<

That just confused me...

[some dude]

Considering in the question it doesn't state when the female ducks lay the eggs, or what we're predicting, for example, the start of the year/end of the year, given that W₀ implies The very beginning, could you argue that you interpreted the question in a way that W₁ is the number of Ducks at the start of the year, given that the equation doesn't say other wise, resulting in The start of the 4th year being >half, and the start of the 5th year being <half, therefore during the 4th year is when the the colony will be halved..

howd you get a hold of the exam? teacher photocopy it or something?

[Natters]

i meant it did state that it represented the beginning of the year

[Deank]

Considering in the question it doesn't state when the female ducks lay the eggs, or what we're predicting, for example, the start of the year/end of the year, given that W₀ implies The very beginning, could you argue that you interpreted the question in a way that W₁ is the number of Ducks at the start of the year, given that the equation doesn't say other wise, resulting in The start of the 4th year being >half, and the start of the 5th year being <half, therefore during the 4th year is when the the colony will be halved..

howd you get a hold of the exam? teacher photocopy it or something?

A teacher got a copy from the exam supervisor

i meant it did state that it represented the beginning of the year

Where!? I must know!

[Natters]

i dont have a copy dude i can't point it our but i remember it being in there
though in hindsight it may have been the birds insects frogs and somethings question

[plato]

These are the last 2 questions.

The breeding matrix B assumes that, on average, each adult female duck lays and hatches two female eggs for each year of the breeding program.
If each adult female duck lays and hatches only one female egg each year, it is expected that the duck colony in the wetland will not be self—sustaining and will, in the long run, die out.
The matrix equation
w(n) = PW(n-1)
with a different breeding matrix
P =  [0            1]
       [0.25   0.5]
and the initial state matrix
W(0) =  [ 32 ]
             [ 64 ]
models this situation.
d. During which year of the breeding program will the number of female ducks in the colony halve?

Changing the number of juvenile and adult female ducks at the start of the breeding program will also change the expected size of the colony.
e. Assuming the same breeding matrix, P, determine the number of juvenile ducks and the number of adult ducks that should be introduced into the program at the beginning so that, at the end of Year 2, there are 100 juvenile female ducks and 50 adult female ducks.

[smithy16]

Apparently with the very last question you were meant to inverse it twice, but i don't understand why? By inversing the numbers for the 2 year, you automatically find the numers for the first year dont you?

[Natters]

i squared it then inversed that
hope it's the same thing

[smithy16]

But why would it be squared? or inversed twice for the matter?

[Deank]

But why would it be squared? or inversed twice for the matter?

Because we want to find the state required for the very beginning (w₀) and the state we get given of 100 Juveniles and 50 Adults is at the end of TWO years, therefore W₂. So if we do T^-1xW₂ we get W₁, so to get W₀, we need to do T^-1xW₁. Hopefully that helps.

[Natters]

you had W(2) and needed W(0)
W(n+1)=PW(n)
so W(1)=PW(0)
W(2)=PW(1)
so W(2)=P(PW(0))
=P^2W(0)
so from that i ended up with W(2)=P^2W(0), W(2) was [[100][50]] or something, whatever they gave us
so (P^2) inversed *[[100][50]] was the W(0), required, for which i got [[400][0]]