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

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Transition Matrices – Using a Certain Rule
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Basic recurrence relation (constant system)

Sn+1=TSnS_{n+1} = TS_n

Extended recurrence relation formula

Sn+1=TSn+BS_{n+1} = TS_n + B

Meaning of TT in transition matrices

Transition matrix showing movement between states

Meaning of BB in extended model

External additions/reductions at each step

Positive values in matrix BB

Additions to the system

Negative values in matrix BB

Reductions from the system

When to use Sn+1=TSn+BS_{n+1} = TS_n + B

When items added/removed regularly from system

Using Sn=TnS0S_n = T^nS_0 for extended model?

Not possible; must calculate step-by-step

Reverse formula for transition matrices

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

Order in Sn+1=TSn+BS_{n+1} = TS_n + B

Calculate TSnTS_n first, then add BB

Explore VCE SSCE General Mathematics Revision Notes by Topics

Setting Up and Interpreting Transition Matrices

Transition Matrices – Using Recursion

Transition Matrices – Using a Certain Rule

Leslie Matrices

Explore VCE SSCE General Mathematics Model Answers by Topics

Setting Up and Interpreting Transition Matrices

Transition Matrices – Using Recursion

Transition Matrices – Using a Certain Rule

Leslie Matrices

Explore VCE SSCE General Mathematics Quizzes by Topics

Setting Up and Interpreting Transition Matrices

Transition Matrices – Using Recursion

Transition Matrices – Using a Certain Rule

Leslie Matrices

Explore VCE SSCE General Mathematics Exam Questions by Topics

Setting Up and Interpreting Transition Matrices

Transition Matrices – Using Recursion

Transition Matrices – Using a Certain Rule

Leslie Matrices

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