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Stitz-Zeager_College_Algebra_e-book

Let a be an arbitrary invertible 3 3 matrix a show

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Unformatted text preview: Show that QXs = Xs This is called the steady state because the number of people who get each paper didn’t change for the next week. Show that Qn X → Xs as n → ∞. (f) Now let S= 2 3 1 3 2 3 1 3 Show that Qn → S as n → ∞. (g) Show that SY = Xs for any matrix Y of the form Y= y 150 − y This means that no matter how the distribution starts in Pedimaxus, if Q is applied often enough, we always end up with 100 people getting the Tribune and 50 people getting the Picayune. 10 More speciﬁcally, we have a Markov Chain, which is a special type of stochastic process. 8.3 Matrix Arithmetic 491 4. Let z = a + bi and w = c + di be arbitrary complex numbers. Associate z and w with the matrices ab cd Z= and W = −b a −d c Show that complex number addition, subtraction and multiplication are mirrored by the associated matrix arithmetic. That is, show that Z + W , Z − W and ZW produce matrices which can be associated with the complex numbers z + w, z − w and zw, respectively. 5. A square matrix is said to be an upper triangular matrix if all of its entries below the main diagonal are zero and it is said to be a lower triangular matrix if all of its entries above the main diagonal are zero. For example, 1 2 3 4...
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