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Wildcat
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Homework Statement
Let A = matrix [a b] row 1 [c d] row 2 (2x2 matrix) with a>0, b>0,c>0,d>0. Show that A has an eigenvector [x,y] (2x1) with x>0, y>0
Homework Equations
The Attempt at a Solution
I've tried finding the characteristic polynomial by using det((lambda)I - A) =0, then using the quadratic equation to find the roots (thats ugly) so I'm trying multipying the column vector x,y by some eigenvalue to get each column of the original matrix.
if c/y is an eigenvalue that corresponds to the eigenvector [ay/c, y] and d/y is an eigenvalue that corresponds to the eigenvector [ by/d , y] a,b,c,d are all >0 therefore the eigenvector values will by >0
Will this work??