Consider the 2 x 2 matrix A = [] and let A (ad) + 4bc....

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Consider the 2 x 2 matrix A ¹ = [] and let A (ad)² + 4bc. Then show that = (a) A is diagonalizable if A > 0. (b) A is not diagonalizable if A <0. (c) If A = 0, then A may be diagonalizable or it may not be. Hint: compute the zeros of the characteristic polynomial of A. To solve c). provide one example for either situation. Problem 9.3. Let A be a diagonalizable matrix. Show that the eigenvalues of A2 are the squares of the eigenvalues of A, but that both A and 4² have the same eigenvectors. Consider the 2 x 2 matrix A ¹ = [] and let A (ad)² + 4bc. Then show that = (a) A is diagonalizable if A > 0. (b) A is not diagonalizable if A <0. (c) If A = 0, then A may be diagonalizable or it may not be. Hint: compute the zeros of the characteristic polynomial of A. To solve c). provide one example for either situation. Problem 9.3. Let A be a diagonalizable matrix. Show that the eigenvalues of A2 are the squares of the eigenvalues of A, but that both A and 4² have the same eigenvectors.

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To prove the given statements lets analyze each part separately a A is diagonalizable if Delta 0 For a 2x2 matrix A a b c d the characteristic polynom... View the full answer