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Finding the Determinant

  1. Apr 3, 2012 #1
    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!:)
     
    Last edited: Apr 3, 2012
  2. jcsd
  3. Apr 3, 2012 #2

    Dick

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    What does the matrix of your linear transformation look like if you express it in the basis {v1,v2,v3,v4}?
     
  4. Apr 3, 2012 #3

    Ray Vickson

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    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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