Q.12. WHICH OF THE GIVEN BELOW ARE ALWAYS TRUE? MAY BE MORE THAN ONE RIGHT ANSWER 1. If A is diagonalizable then cA is diagonalizable for any constant of c. 2. If the characteristic polynomial of a diagonalizable matrix A is equal to (A – 7)^(3))((A – 5)^(6))((A – 8)^(2)) then the eigenvalue A = 7 has a geometric multiplicity of 3. 3. If A is similar to B, then AT is similar to B.

Q.12. WHICH OF THE GIVEN BELOW ARE ALWAYS TRUE? MAY BE MORE THAN ONE RIGHT ANSWER 1. If A is diagonalizable then cA is diagonalizable for any constant of c. 2. If the characteristic polynomial of a diagonalizable matrix A is equal to (A – 7)^(3))((A – 5)^(6))((A – 8)^(2)) then the eigenvalue A = 7 has a geometric multiplicity of 3. 3. If A is similar to B, then AT is similar to B.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.CR: Review Exercises

Problem 64CR: a Find a symmetric matrix B such that B2=A for A=[2112] b Generalize the result of part a by proving...

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