Question

.Let M = (6 6). 12

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A) Calculate det(M) . What does this tell you about M(∎), where ∎ is the unit square: 0≤ ? ≤ 1, 0 ≤

? ≤ 1.

B) Find the eigenvalues and associated eigenspaces for M. C) Find an eigenbasis for R2 using M.

D) Find C and C-1 such that C-1MC = D is diagonal.

E) Use D) to calculate Mn.

F) Use D) to calculate eMt.

G) Find lim Mn [1] ?→∞ 1

H) Describe what happens to Mn[1] as n->∞. 0

I) Describe what happens to eMt as t->∞

Answer 1

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