Let A be a 4 × 4 matrix and suppose that A is a diagonalizable. If the characteristic polynomial of A is ca(x) = (x + 1)(x – 1)³ then which of the following are true?

Q: If A is a 2 × 2 matrix, prove that the characteristic polynomial of A is χ(λ) = λ2 − (trA)λ + (det…

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Q: Find the characteristic polynomial of the matrices

A: A=4-13021003 Now consider,…

Q: Find the characteristic polynomial of the matrix, A= (3−12−624−312),then verify Cayley-Hamilton…

A: We have to find A inverse

Q: Find the characteristic polynomial of the matrices

A: we have to find  the characteristic polynomial of the matrices A=21-13

Q: 3. (a) If A be an n x n invertible matrix. Prove that the inverse of A is unique.

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Suppose that the characteristic polynomial of a matrix A is p(A) = A(A² − 6A + 9). A will have…

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Q: Let [1 0.25] A : 1 Find an invertible matrix X and a diagonal matrix D such that X-'AX = D.

A: If for matrix A,      X-1 AX =D  Then matrix A is Diagonalisable,   And where D is diagonal matrix…

Q: Let X be any n x k matrix. Show that X'X is a symmetric matrix.

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Q: Pls explain to me step by stepThanks

A: The given matrix is

Q: Show that if A is a square matrix such that A? = A, then the minimal polynomial of A is m(t) = t,…

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Q: Find the characteristic polynomial of the matrix 1 -2 A = -1 -3 3

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Q: 5 3/3 Let A= The characteristic polynomial of matrix A is ... 3/3 -1

A: Given,

Q: determine whether the given matrix is defective or nondefective.

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Q: Show that the characteristic polynomial of A is p(λ)=λ2−5λ+6.

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Q: Let A be a 2 ×2 matrix and let p(λ) = λ2 + bλ + c be the characteristic polynomial of A. Show that b…

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Q: Find the characteristic polynomial of the matrix 3 -5 A = 1 -2 -5 3 2(x) =D

A: Given,            A=3-5001-2-530

Q: a) suppose A is a 3x3 matrix with the characteristic polynomial pld) = -d? (At3), If A is…

A: Given, matrix A is diagonalizableand characteristics polynomial of Ap(λ)=-λ2(λ+3)We can find…

Q: Find the characteristic polynomial of the matrix p(x) = de. = A 0 -2 -2 0 5 -3 -1 0

A: Given matrix is A = -5-2005-1-2-30

Q: Find the characteristic polynomial of the matrix 4 5 0 A = 4 3 -4 4 0 p(x) =

A:

Q: Let P be an m × m matrix with entries in the polynomial algebra F [x]. L:1.1.

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Q: A is a square matrix and p(A) = det (Al – A) is the characteristic polynomial of A, then the…

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Q: Find the characteristic polynomial of the matrix -9 A = 1 p(z)

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Q: If A is an  m × n matrix with entries in the field F, then                   row rank (A) = column…

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Q: Let A be an n x n matrix such that Am = 0 for some positive integer m. Show that A is not…

A: A is a n×n invertible matrix, such that Am=0⋯⋯1 Taking determinants both side, detAm=det0detAm=0…

Q: 5. Let A be a (3×3)-matrix with the characteristic polynomial pA(x) = (2 – x)(x² + 1– a²) for some a…

A: Solution (a):- Given Characteristic polynomial of matrix A =  (2-x)(x2+1-a2) But we have to find the…

Q: Find the characteristic polynomial of the matrix 2 1 01 A =0 3 3 4 3 p(x) =

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Q: Find the characteristic polynomial of the matrix 3 -2 A = 4 -3 2 4 p(x) =

A: Given matrix is A = 3-2004-3240

Q: Please see image

A: A being characterstic polynomial follows, |A-tI|=f(t)

Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 7A +…

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Q: If you carefully track the definition of the minimal polynomial of a linear operator or matrix, you…

A: If A∈Mn×nℝ and let m1x is minimal polynomial of A over ℝ. And m2x be the minimal polynomial of A…

Q: 2. Let A be an n xn nonsingular matrix with entries from a field F. Suppose that the vectors v1,...…

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Q: If A is a 2 x2 matrix such that det(A) = -3 and tr(A) = 5 then the characterestic polynomial of A is…

A: For a matrix abcd the characterstic polynomial is λ2-tr(A)λ+det(A)Given tr(A)=5 and det(A)=-3

Q: Suppose A is an n×n invertible matrix such that A – 2A = I, . Find an for A. expression

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Q: Find the characteristic polynomial of the matrix p(x) = || 5 -2 0 419 A = 0 -4 0

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Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 2A +…

A: Finding such a is equivalent to finding a 2 by 2 matrix with trace -2 and determinant 5. As in…

Q: Find the characteristic polynomial of the matrix 2 A : 4 -4 -4 p(x) =

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Q: Find the characteristic polynomial of the matrix 1 3 A = -1 -4 -4 4 p(æ) =

A: Where we have to find out the characteristic polynomial of a given matrix

Q: Let A be a symmetric 2 X 2 matrix and let k be a scalar. Prove that the graph of the quadratic…

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Q: If the characteristic polynomial of a matrix A is p(2) = 23 – 522 + 62. Then tr(A)

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Q: Find the companion matrix of p(x) = x2 -7x + 12 and then find the characteristic polynomial of C(…

A: Consider the given function is P(x)=x2-7x+12. Then, the companion matrix is, C(P)=7-1210 Thus, the…

Q: Find the characteristic polynomial of the 3 x 3 matrix, A, where

A: A matrix is a mathematical object containing numbers arranged in rows and columns. If the number of…

Q: Suppose that the characteristic polynomial of a matrix A is: p(λ) = λ (λ2−6λ+12) (λ+1) Which of…

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Q: 2. If the characteristic polynomial of a matrix A is p(2) = 23 – 522 + 62. Then tr(A) = None -5 11…

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Q: Find the characteristic polynomial of the matrix [-10 6] A = 10 p(z) =

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Q: If A is a 2 x2 matrix such that det A) = - 3 and tr(A) =5 then the characterestic polynomial of A is…

A: The characteristic polynomial is, p(λ) = λ² - (tr A) λ + (det A)  Given, det(A) = -3 and tr(A) = 5

Q: Show that A and B are not similar matrices. 2 1 , В 3 3 -1 A = -3 7 -6 Since A has characteristic…

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Q: Find the characteristic polynomial of the matrices

A: Given: Let A=121012-132 To Find: Characteristic polynomial of the given matrices

Q: Find the characteristic polynomial of the matrix -3 1 A = -3 -1 -3 -4 p(x) =

A: Given problem is :