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Asked Sep 23, 2019
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26) If A and B are similar matrices, then they have:
Same eigenvalues.
Same eigenvectors.
I.
II.
III.
Same trace.
IV.
Same determinant.
Same characteristic polynomial
V.
A) I, III, IV, V
B) I,П, II
C) I, III,IV
D) III, IV, V
E) I,II, III, IV, V
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26) If A and B are similar matrices, then they have: Same eigenvalues. Same eigenvectors. I. II. III. Same trace. IV. Same determinant. Same characteristic polynomial V. A) I, III, IV, V B) I,П, II C) I, III,IV D) III, IV, V E) I,II, III, IV, V

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Expert Answer

Step 1

Similar matrices have same determinant.

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det(B) det(PAP) - det (pPA) "'"PА = det(LA) = -det(A)

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Step 2

Similar matrices then they have same trace.

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Tr(B) Tr(P AP) -Tr(p PA) Tr(IA) =r(A)

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Step 3

Given that A and B are similar matrices then th...

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PAP B det (B-) det(PAP-AI) det(B-I) detP(A-)P) det (B-I det(A-) detPAP = det A for invertible matrix P =

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