Transition Matrices – Using a Certain Rule (VCE SSCE General Mathematics): Quizzes

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Transition Matrices – Using a Certain Rule
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What does the extended model Sn+1=TSn+BS_{n+1} = TS_n + B account for that the basic model does not?

External additions or reductions

In the relation Sn+1=TSn+BS_{n+1} = TS_n + B, what does matrix BB represent?

External additions or reductions

What do positive values in matrix BB represent?

Additions to the system

When should you use Sn+1=TSn+BS_{n+1} = TS_n + B instead of Sn+1=TSnS_{n+1} = TS_n?

When items are added or removed regularly

Can you use Sn=TnS0S_n = T^nS_0 as a shortcut for Sn+1=TSn+BS_{n+1} = TS_n + B?

No, must calculate step-by-step

What is the reverse formula for Sn+1=TSn+BS_{n+1} = TS_n + B?

Sn=T−1(Sn+1−B)S_n = T^{-1}(S_{n+1} - B)

In calculating Sn+1=TSn+BS_{n+1} = TS_n + B, which operation must be performed first?

Matrix multiplication TSnTS_n

If T=[0.80.10.20.9]T = \begin{bmatrix} 0.8 & 0.1 \\ 0.2 & 0.9 \end{bmatrix}, what % of Bendigo cars stay in Bendigo?

80%80\%

Given S0=[5040]S_0 = \begin{bmatrix} 50 \\ 40 \end{bmatrix}, T=[0.80.10.20.9]T = \begin{bmatrix} 0.8 & 0.1 \\ 0.2 & 0.9 \end{bmatrix}, B=[22]B = \begin{bmatrix} 2 \\ 2 \end{bmatrix}, find cars at Bendigo after 1 week.

4646

When should you use the reverse formula Sn=T−1(Sn+1−B)S_n = T^{-1}(S_{n+1} - B)?

When you know a later state, need earlier

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