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VCE 12 General 2023

7.07 Transition matrices

Interactive practice questions

Let $A=$A=   $5$5 $7$7  
  $8$8 $6$6  

Use your calculator to find the following powers of $A$A:

a
$A^2=$A2=   $\editable{}$ $\editable{}$  
  $\editable{}$ $\editable{}$  
b
$A^3=$A3=   $\editable{}$ $\editable{}$  
  $\editable{}$ $\editable{}$  
c
$A^4=$A4=   $\editable{}$ $\editable{}$  
  $\editable{}$ $\editable{}$  
Easy
1min

For the matrices $A$A, $B$B and $C$C, use technology to calculate:

Easy
4min

The following two states, $A$A and $B$B, and their transition probabilities are displayed in the diagram below.

Easy
< 1min

For two states $M$M and $N$N, the percentage of each population that will transition to either state in the next period, are displayed in the diagram below.

Easy
< 1min
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Outcomes

U4.AoS2.2

the inverse of a matrix and the condition for a matrix to have an inverse, including determinant for transition matrices, assuming the next state only relies on the current state with a fixed population

U4.AoS2.4

transition diagrams and transition matrices and regular transition matrices and their identification

U4.AoS2.5

use matrix recurrence relations to generate a sequence of state matrices, including an informal identification of the equilibrium or steady state matrix in the case of regular state matrices

U4.AoS2.6

construct a transition matrix from a transition diagram or a written description and vice versa

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