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: Suppose that A is a 3 x 3 matrix with the following properties: 4 -5 is an eigenvector for A…

A: Given that A is a 3×3 matrix with the following properties :  u = 4-5-1 is an eigenvector for A…

Q: A = X 1 and B = [X = [11] 0 L1 alue of x that make BxA is Eigen matrix

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A: Given that, The characteristic polynomial of a matrix A is:px=x3-2x2+x+5, where x is the eigenvalue…

Q: 1. (9pts) Diagonalize the matrix below by the following steps: 2 2 A: 1 3 -1 eigenvalues are λ = 5,…

A: Step 1: Step 2: Step 3: Step 4:

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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: 1 3 - Q5. Let A be the 2 × 2 matrix 1 1 (a) Find an eigenbasis B for A. (b) Find the B-matrix for A.…

A: As your question contains multiple subpart, so I only first 3 subparts.

Q: Suppose that some 3x3 matrix A has a characteristic polynomial (2 – A) (5 – A) What are the…

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A: We have to show that  have same eigenvalues using given data.Concept required:Eigenvalues of are…

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Q: O True O False

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Q: 2. Consider the quadratic form Q(r)=-6s²-10st-61². (i) Find the corresponding symmetric matrix. (ii)…

A: According to the guideline only three subpart can be answered. Please post other questions…

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Q: The charactertistic polynomial of the matrix C = is p(x) = x²(x - 1). The matrix has two distinct…

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Q: こ Find all eigenvectors of the the matrix A= 4 1 2 3 (a) ; (d) ; (b) ; (c) ; C O b

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Q: If A is an nxn matrix, then the eigenvalues can be determined by

A: Given that if A is an n×n matrix, then our aim is to tell how eigen valuescan be determined?

Q: Suppose that A is a 3-by-3 real matrix with an eigenvalue of 2. If the characteristic polynomial of…

A: As we know that Eigen values are the roots of the characteristic polynomial Given characteristic…

Q: 2. Find the eigenvalues of the following matrix: 2x, = 9 -X, + 2x, -X, + 2x, x, = 8 3 Is the matrix…

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