and suppose A is a 3 x 3 matrix such 3 11. Let X1 , X2 = ,X3 1 that Axı = 2x1, Ax2 = 2x2, Ax3 = X3 (a) Find the eigenvalues and eigenvectors of A. (b) Find 3 x 3 matrices P and D such that D is diagonal and D = P-'AP.

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A: J

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Q: (e)  Show that the matrix is diagonalizable and find an invertible matrix P and a diagonal matrix D…

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Q: 35. Give an example of a 4 x 4 matrix A without real eigen- values. ANS: Го -1 07 1 A = 0 0 -1 0 1

A: The answer is given as follows.

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A: To Find: a 3×3 matrix whose 4-eigenspace is V=x, y, z in ℝ3 | -8x-14y+10z=0 and whose 3-eigenspace…

Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-'AP is diagonal. (If not…

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