Let 1 3 4. A = -5 -3 and B = -4 -6 -3 3 1 3 1 For this problem, you may use the fact that both matrices have the same characteristic polynomial: PA(A) = PB(A) = -(A – 1)(A+2)². (a) Find all...

Let<br>1<br>3<br>4.<br>A =<br>-5<br>-3 and B =<br>-4<br>-6<br>-3<br>3<br>1<br>3<br>1<br>For this problem, you may use the fact that both matrices have the same characteristic polynomial:<br>PA(A) = PB(A) = -(A – 1)(A+2)².<br>(a) Find all eigenvectors of A.<br>(b) Find all eigenvectors of B.<br>(C) Which matrix A or Bis diagonalizable?<br>(d) Diagonalize the matrix stated in (C), i.e., find an invertible matrix P and a diagonal matrix D such that A = PDP<br>B= PDP 1.<br>1<br>or<br>%3D<br>%3D<br>

Extracted text: Let 1 3 4. A = -5 -3 and B = -4 -6 -3 3 1 3 1 For this problem, you may use the fact that both matrices have the same characteristic polynomial: PA(A) = PB(A) = -(A – 1)(A+2)². (a) Find all eigenvectors of A. (b) Find all eigenvectors of B. (C) Which matrix A or Bis diagonalizable? (d) Diagonalize the matrix stated in (C), i.e., find an invertible matrix P and a diagonal matrix D such that A = PDP B= PDP 1. 1 or %3D %3D

Jun 03, 2022

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Let 1 3 4. A = -5 -3 and B = -4 -6 -3 3 1 3 1 For this problem, you may use the fact that both matrices have the same characteristic polynomial: PA(A) = PB(A) = -(A – 1)(A+2)². (a) Find all...

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