Three Applications of Matrix Algebra

Matrix algebra and n - D Vector transformations:

Example: $\QTR{Large}{n=2}$

Multiply MATH by MATH and MATH .

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Markov Processes:

Example: Suppose that the matrix MATH represents the probabilities that, if it is rainy or sunny on a given day(Column) it will be

rainy or sunny on the next day(Row). Suppose that MATHis the probability that it rainy or sunny on Wednesday, what is the probability that it will be rainy or sunny on Thursday? Friday?

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Paths and Hops:

MATH

The associated Matrix

A B C D E F G

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MATHM MATH

M MATH MMATH