College Algebra question about determinants, please help
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College Algebra question about determinants, please help

[From: ] [author: ] [Date: 12-04-04] [Hit: ]
thanks!AP = PD,......
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>, <0,0,1,1>

Calculate |A|
Hint: For nxn matrices X, Y , Z
|XYZ| = IXI IYI IZI and IX^ (-1)I= 1 / IXI

any input or ideas of how to start this problem will be helpful
thanks!

-
Since there are 4 distinct eigenvalues
AP = PD, A = PDP ֿ ¹
detA = detP * detD * 1/detP = 2 * 1 * ½ * 10 = 10
1
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