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Finding the Determinantby deana
Tags: determinant 
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#1
Apr312, 06:36 PM

P: 3

1. The problem statement, all variables and given/known data
Let A be the matrix with eigenvalues x1 = 2, x2 = 1, x3 = 1/2 , x4 = 10 and corresponding eigenvectors v1: <1,1,1,0>, v2: <1,1,0,0>, v3: <1,0,0,1>, v4: <0,0,1,1> Calculate A 2. Relevant equations See above 3. The attempt at a solution I'm not really sure how to start this problem but i know that: For nxn matrices X, Y , Z XYZ = X Y Z and X^ (1)= 1 / X Maybe I could use this to solve the problem? Any input or suggestions about how to start this problem would be helpful! Thanks!:) 


#2
Apr312, 06:40 PM

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P: 25,228

What does the matrix of your linear transformation look like if you express it in the basis {v1,v2,v3,v4}?



#3
Apr312, 07:58 PM

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P: 5,081

Do you know the relationship between the eigenvalues of a matrix and the determinant of that matrix? It is a standard result. If it is not in your textbook or course notes, it can certainly be found through Google.
RGV 


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