Project - Woozle Study

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Reference no: EM132412029

Project - Woozle Study

Let W be the 5 x 5 matrix from the data attached, where each entry is a probability between 0 and 1 rather than a percentage:

2448_figure.png

PROBLEM 1. Observe that Wn = n where n =680_figure1.png. Explain why this makes sense.

PROBLEM 2. Observe that WTp≈p where p =790_figure2.png. Explain why this makes sense.

PROBLEM 3. Let I denote the 5 x 5 identity matrix.

(a) Find all solutions x to the equation Wx = x. What is the rank of the matrix W - I?

(b) Find all solutions x to the equation WTx = x. What is the rank of the matrix WT - I?

(c) Explain why it is not a coincidence that the rank of W - I and WT - I are the same.

PROBLEM 4. Think of a process that Christopher might have used to calculate the percentage of time that woozle spend doing each activity. If your answer involves solving a certain system of linear equations, explain how Christopher could anticipate that the system is consistent.

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Reference no: EM132412029

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