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Introduction to this Tutorial
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Sets and Set Notation
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Proof of the Infinitude of Primes
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Boolean Set Operations
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Vectors and Vector Operations
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Introduction to Vectors (5:11)
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Scalar Multiplication (6:41)
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Vector Addition (4:32)
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Quiz #4
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Quiz #4 Solution
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The Dot Product (6:00)
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Quiz #5
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Quiz #5 Solution
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Geometric Interpretation of the Dot Product (6:39)
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The Dot Product and Projections (8:26)
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Quiz #6
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Quiz #6 Solution
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The Cross Product, Part I (8:06)
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The Cross Product, Part 2 (4:05)
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Quiz #7
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Quiz #7 Solution
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Matrix Operations
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Essential Types of Matrices
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Vector Spaces
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Determinants
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Diagonalization and Powers
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Geometric Transformations
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Differentiation as a Matrix Operation
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3.4 Markov Chains » Quiz #21 Solution
From the information given in the problem, it follows that the stochastic/transition matrix is: . Note that the columns sum to 1, as required. Furthermore, we observe that the P matrix is additionally 'regular', which indicates the existence of a unique, steady-state vector corresponding with P. In order to find the steady state vector v, we solve the system
for the vector v. The result is
.