Find an invertible matrix P and matrix C such that C = P-1AP.
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Find the eigenvalues of A. Hint: Use the fact that the trace…
Find the eigenvalues of A. Hint: Use the fact that the trace of A (sum of the entries on the main diagonal of A) should equal the sum of the eigenvalues (including multiplicities) to check your answer.
If a 3×3 matrix A has fewer than 3 distinct eigenvalues, the…
If a 3×3 matrix A has fewer than 3 distinct eigenvalues, then A is not diagonalizable.
The matrices A and AT have the same eigenvalues, counting mu…
The matrices A and AT have the same eigenvalues, counting multiplicities.
Find the characteristic polynomial of A. Do not factor your…
Find the characteristic polynomial of A. Do not factor your answer.
Similar matrices have the same eigenvalues.
Similar matrices have the same eigenvalues.
If A is row equivalent to the identity matrix, then A is dia…
If A is row equivalent to the identity matrix, then A is diagonalizable.
Is A diagonalizable? Explain.
Is A diagonalizable? Explain.
Eigenvalues must be nonzero scalars.
Eigenvalues must be nonzero scalars.
Each eigenvalue of A is also an eigenvalue of A2.
Each eigenvalue of A is also an eigenvalue of A2.