A real 3 × 3 matrix A has eigenvalues −.5, .2 + .3i, and .2 − .3i, with corresponding eigenvectors
v1 =
1. Is A diagonalizable as A = PDP−1, using complex matrices?
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- For what values of a does the matrix A=[01a1] have the characteristics below? a A has eigenvalue of multiplicity 2. b A has 1 and 2 as eigenvalues. c A has real eigenvalues.arrow_forwardDefine T:P2P2 by T(a0+a1x+a2x2)=(2a0+a1a2)+(a1+2a2)xa2x2. Find the eigenvalues and the eigenvectors of T relative to the standard basis {1,x,x2}.arrow_forwardConsider again the matrix A in Exercise 35. Give conditions on a, b, c, and d such that A has two distinct real eigenvalues, one real eigenvalue, and no real eigenvalues.arrow_forward
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