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Unformatted text preview: Math 464, Worksheet 10 The goal in this worksheet is to compute a high power of a matrix. For example, bracketleftbigg . 95 . 1 . 1 . 89 bracketrightbigg 500 The process involves eigenvalues and eigenvectors , which I will define by example as they come up, and them more formally in the next worksheet. Part I. The first stage is to solve the system of two equations bracketleftbigg . 95- . 1 . 1 . 89- bracketrightbigg bracketleftbigg x y bracketrightbigg = bracketleftbigg bracketrightbigg for the three variables x , y and . Thats more than 2 variables, so we dont use normal algebra to solve this. Instead: Any solution with x = 0 and y = 0 is forbidden. Other solutions exist if and only if the determinant of bracketleftbigg . 95- . 1 . 1 . 89- bracketrightbigg is zero. Therefore: 1. Solve the equation ( . 95- )( . 89- )- ( . 1)( . 1) = 0 Each solution is called an eigenvalue ....
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