- #1
derryck1234
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Homework Statement
Let B = 1 0
6 -1
Be a square matrix. Find a non-singular matrix P such that P-1BP = D, where D is a diagonal matrix and show that P-1BP = D.
Homework Equations
det(lambdaI - A) = 0
The Attempt at a Solution
Ok, this might look like a simple problem...but I get non-linearly independent eigenvectors, even although I have 2 distinct eigenvalues?
Noting that it is a triangular matrix, the diagonal entries thus correspond to its eigenvalues. So, the matrix has lambda = 1 and lambda = -1 as its eigenvalues.
For lambda = 1, I obtain the basis vector (1/3, 1).
For lambda = -1, I obtain the basis vectors (1, 0) and (0, 1)...
Thus, I have non-linearly independent eigenvectors, since (1/3, 1) can be written as 1/3(1, 0) + (0, 1)...
?