Last updated on Jun 09, 2026

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

Practise the questions

10 questions from this quiz

Explore VCE SSCE General Mathematics Revision Notes by Topics

Explore VCE SSCE General Mathematics Model Answers by Topics

Explore VCE SSCE General Mathematics Flashcards by Topics

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

Practise the questions

Explore VCE SSCE General Mathematics Revision Notes by Topics

Explore VCE SSCE General Mathematics Model Answers by Topics

Explore VCE SSCE General Mathematics Flashcards by Topics

Join 100,000+ SSCE students studying Quizzes with us.

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

Practise the questions

What does the extended model Sn+1=TSn+BS_{n+1} = TS_n + BSn+1​=TSn​+B account for that the basic model does not?

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

What do positive values in matrix BBB represent?

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

Can you use Sn=TnS0S_n = T^nS_0Sn​=TnS0​ as a shortcut for Sn+1=TSn+BS_{n+1} = TS_n + BSn+1​=TSn​+B?

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

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

If T=[0.80.10.20.9]T = \begin{bmatrix} 0.8 & 0.1 \\ 0.2 & 0.9 \end{bmatrix}T=[0.80.2​0.10.9​], what % of Bendigo cars stay in Bendigo?

Given S0=[5040]S_0 = \begin{bmatrix} 50 \\ 40 \end{bmatrix}S0​=[5040​], T=[0.80.10.20.9]T = \begin{bmatrix} 0.8 & 0.1 \\ 0.2 & 0.9 \end{bmatrix}T=[0.80.2​0.10.9​], B=[22]B = \begin{bmatrix} 2 \\ 2 \end{bmatrix}B=[22​], find cars at Bendigo after 1 week.

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

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 Flashcards by Topics

Setting Up and Interpreting Transition Matrices

Transition Matrices – Using Recursion

Transition Matrices – Using a Certain Rule

Leslie Matrices

Join 100,000+ SSCE students studying Quizzes with us.

What does the extended model $S_{n+1} = TS_n + B$ account for that the basic model does not?

In the relation $S_{n+1} = TS_n + B$ , what does matrix $B$ represent?

What do positive values in matrix $B$ represent?

When should you use $S_{n+1} = TS_n + B$ instead of $S_{n+1} = TS_n$ ?

Can you use $S_n = T^nS_0$ as a shortcut for $S_{n+1} = TS_n + B$ ?

What is the reverse formula for $S_{n+1} = TS_n + B$ ?

In calculating $S_{n+1} = TS_n + B$ , which operation must be performed first?

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

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

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