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Perform the Markov Chain with:
Transition Matrix A and initial state vector B

Since |A| is a 3 x 3 matrix
and |B| is a 3 x 1 matrix,
|AB| will be a 3 x 1 matrix

P⁽¹⁾ = TP⁽⁰⁾

Green Answer Entry for Row 1, Column 1

Multiply red row 1 entries in |A|
by the blue column 1 entries in |B|
to get answer entry |AB₁₁|

1	2	3
4	5	6
7	8	9

x

9

6

3

=

30

|AB₁₁| = A₁₁ x B₁₁ + A₁₂ x B₂₁ + A₁₃ x B₃₁
|AB₁₁| = 1 x 9 + 2 x 6 + 3 x 3
|AB₁₁| = 9 + 12 + 9
|AB₁₁| = 30   ← Green Answer Entry

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Green Answer Entry for Row 2, Column 1

Multiply red row 2 entries in |A|
by the blue column 1 entries in |B|
to get answer entry |AB₂₁|

1	2	3
4	5	6
7	8	9

x

9

6

3

=

30

84

|AB₂₁| = A₂₁ x B₁₁ + A₂₂ x B₂₁ + A₂₃ x B₃₁
|AB₂₁| = 4 x 9 + 5 x 6 + 6 x 3
|AB₂₁| = 36 + 30 + 18
|AB₂₁| = 84   ← Green Answer Entry

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