Which of the following statements are always true? (i) If A is a 3 × 3 diagonalizable matrix then A has 3 distinct eigenvalues. (ii) If the characteristic polynomial of a matrix A is equal to (1 – 3)*(2 – 6)°(2 – 7)8 then the eigenvalue 2 has a geometric multiplicity of 4. (iii) If A is similar to B, and B is symmetric, then A' is similar to B. = 3 A) (i) and (ii) only (B) (ii) and (iii) only (C) (ii) only (D) none of them (E) (iii) only (F) (i) only G) all of them (H) (i) and (iii) only

Q: Let A be a 6 x 6 matrix with characteristic polynomial det(AI – A) = (1 – 2)*(1 – 4)². Without…

A: Given that, A is a 6×6 matrix with characteristic polynomial detλI-A=λ-24λ-42

Q: [2 1 4. Let A = 1 1 -1 2 -1 2 Show that the characteristic polynomial fa of A is -X³ + 5A² – 21 – 8.…

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Q: 4. True or false For each part, determine if you believe the statement is true or false, and justify…

A: To check whether given statement is true or not.

Q: 3. Suppose that the characteristic polynomial of a square matrix A is fA(^) = –X³ + 3A (a) What is…

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve first three…

Q: 9. (BH) Consider the following matrix: 1 0 -1 F = -4 5 4 2 0 -2 We wish to calculate the eigenvalues…

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Q: Consider the following matrix: -6 -1 2 A 3 2 0 -14 -2 5 Whose characteristic polynomial is p(A) =…

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Q: trix

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Q: 13. Give examples of matrices satisfying the properties below. (a) A has size 2 × 2 and 1,2 are…

A: NOTE: Since we can solve at most three subparts in a question, we have solved the first three…

Q: Suppose A = 3 6 <-2 0 1 -1 3 0 0 (1) Find the characteristic polynomial and all the eigenvalues of…

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Q: (1) If A is diagonalizable then cA is diagonalizable for any constant c. (i1) If the characteristic…

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Q: For the symmetric matrix 1 2 21 A = 200 (2 0 2/ find a diagonal matrix D and an orthogonal matrix P…

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Q: Which of the following statements is(are) true if

A: Introduction: Only zero and one are the eigenvalues of the identity matrix and the zero matrices,…

Q: A is a 3 x 3 matrix with eigenvectors v₁ = Write x as a linear combination of the given…

A: For a matrix A with eigen vector x for eigen value a we have Ax=ax. see below the answer and…

Q: Write whether the following statements are true or false with the whole word. (a) (5) If M is a…

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Q: The scalar λ = 3 is an eigenvalue for the matrix 4 -2 5 –4 0 8 -10 15 3 -1 8 3 2 -1 4 4 Compute the…

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Q: Let A be a 9 x 9 matrix with characteristic polynomial det(AI – A) = (1 – 3)*(1 – 4)²(1 – 5)³.…

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Q: (d) Hence find a fundamental set of solutions r(1)(t), x(2)(t) and a fundamental matrix F(t) for the…

A: Note: As per the question, parts (d), (e), and (f) will be calculated by taking A as any arbitrary…

Q: Suppose A is a 2 x 2 real matrix that has two eigenvalues A₁ and ₂, and X₁ is not equal to X₂.…

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Q: 2. Without using Sage, find • the characteristic polynomial the eigenvalues (include the…

A: Since you have asked multiple questions, we can solve first question for you. If you want other…

Q: (d) The characteristic polynomial of A is –t(t² – t + 6). (e) The characteristic polynomial of A is…

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Q: If A is a Hermitian matrix, then A has both real and complex eigenvalues. A has only real…

A: In this question it is given that A is a Hermitian matrix. A hermitian matrix is a square matrix…