AP Precalculus / Unit 4: Functions Involving Parameters, Vectors, and Matrices
4.14 Matrices Modeling Contexts
Notes
A transition matrix models how amounts move between states each step: $\vec s_{n+1}=A\vec s_n$.
- Columns (or rows) sum to 1 for probabilities.
- Predict later states by multiplying repeatedly: $A^n\vec s_0$.
Practice
$\vec s_1=A\vec s_0$. Then $\vec s_3=$
Apply $A$ three times.
In a probability transition matrix, each column sums to:
Everything goes somewhere.
80% of customers stay with brand X and 20% switch to Y each month. The entry for X to X is:
The stay probability.
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