[2 1 4. Let A = 1 1 -1 2 -1 2 Show that the characteristic polynomial fa of A is -X³ + 5A² – 21 – 8. Note: fa factors as -(A – 4)(A – 2)(A + 1). You don't have to show this. 4 0 0 2 (b) Let D = Find an orthogonal matrix S so that A = SDS". 0 0 Express e in coordinates with respect to the columns of S.

Q: For the characteristic polynomial of Matrix A, p(x) = x³ - 2x² + x + 5, where xis the Eigen value of…

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

Q: -4 4 The characteristic polynomial for the matrix F 3 -4 7 -3 6 is Af(t) = (t – 3)²(t – 1). Find…

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Q: Given the matrix A = -1 1 -1 0-2 1 2 0 1 (a) Find the singular values o, of A. [Hint: first show…

A: Given: A=-11-10-21201 (a) To find the singular values of A.

Q: 5. 2. Let g = |4i 1 0 Find matrix h e GL3(C) such that h¯'gh is in the Jordan normal form. 0 1

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Q: 1 2 2 1 -2 1 . Find the characteristic polynomial A4(t) for the matrix A -3 2 -1

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Q: 5 4 2 3. Consider the matrix A = 4 5 2. 2 2 2 (a) Find the characteristic polynomial det(A– AI) = 0,…

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Q: (b) Find the characteristic equation of the matrix P defined by [2 1 11 P = 1 2 1 li 1 21 Further…

A: The given matrix is P=211121112  the characteristic equation is given by P-λI=0 where I is the…

Q: 3. Suppose T E L(R*) is defined by 2 -6 9. Tr = -6 2 -9 1, Z ER³. -2 2 -4 The eigenvalues of T are…

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Q: 9 Suppose V is finite-dimensional, T e L(V), and v e V with v 0. Let p be a nonzero polynomial of…

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Q: 8.C.7: Suppose V is a complex vector space. Suppose that PE£(V) is such that P2 =P. Prove that the…

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Q: 5 2 1 What is the coefficient of X? in the characteristic polynomial of the matrix A = 1 1 2 ? 15 2

A: Given : 5211127152

Q: 6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = -Ĵa cos(xt) f(t) dt. Show that (i) T is…

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Q: [1 2 8. Let A = and define Q : R² → R by Q(x) = x"Ax. 2 1 (a) Find the characteristic polynomial of…

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Q: d. Suppose that the characteristic polynomial of a matrix A is det(A – AI) = -1³ + 4A. What are the…

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 3 4 Find the characteristic polynomial p(A)of the matrix A = Op(A) = 12 ++6 Op(A) = x? +A– 10 Op(A)…

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Q: If the characteristic polynomial of a matrix A is fA(t) = (t + 1)*(t – 2)(t – 4), what is the size…

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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: Let A = a. By diagonalization of A, compute e^. b. Find ao, a1 so that e4 = aoI+ a1A. c. The…

A: Given that A=5-131 Now we have to find eA

Q: Which of the following is true for the matrix? 2 -1 The eigenvalues ofl. A are -1 and 5. I1. An…

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Q: 4. For the matrix 1 X' = 1 1 1 4 -2 3 -5 compute P = X(X'X)-1X' and M =I- P (a) Verify that MP = (0.…

A: Consider the provided matrix, X'=11114-23-5For to find P=XX'X-1X' ,X=14 1-2 13 1-5

Q: Suppose that a 4 x 4 matrix A has eigenvalues A₁ = 1, A₂=-2, A3=5, and A4 =-5. Use the following…

A: To solve this problem ,we use the below concepts  1) use the method mention in the given question.…

Q: 3 1 4 11 0 2 5 7 9 B) Consider the matrix A =0 052 6 00 0 5 5 Lo 0 0 0 5 Write down the…

A: The given matrix is                                      A=1314102579005260005500005

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: The matrix T has eigenvalues and eigenvectors: • v = 1 with A =1. -1 1 with = 0. • V3 with A- Sive…

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Q: Q1 For the given matrix M. Find the Eigen values and their corresponding vectors. sin n/2 2 cos 2n…

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Q: Suppose that the matrix A has a characteristic polynomial given by p(A) = (A − 6)³ (A + 2)5 (A + 1).…

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Q: Let Pr) = r - 4r + ar+ 30 be the characteristic polynomial of 3 x 3 matrix A, where a is a real…

A: We will find out the required eigen value of matrix A.

Q: Consider the matrix A = ol: The characteristic polynomial of A is p(A) = X² –A-1. What happens when…

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Q: Given the following matrix: A = 1 -1 4 -1 2 0 1 3 -1 Complete the following: a) Its characteristic…

A: Please see the below pictures for detailed solution.

Q: Let A be 2 x2 matrix with tr(A)=4, det(A)=5,then the characteristic polynomial of A is: Select one:…

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Q: 4. Let T € L(P2(C)) be defined by Tp = p(-1) + p(0)z + p(1)z?, for p = ao + ajz + azz? € P2(C). Find…

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Q: A matrix A € M4 (R) has rank 2. Which of the following cannot be the characteristic polynomial of A?…

A: This question is related to characteristic polynomial and eigen values of matrix.

Q: 0 -1 Let B =|-1 L-1 -1] 1. Given that the characteristic ol 1 polynomial of B is (1 + 1)²(1 – 2)…

A: We have to find the value of Q  matrix.

Q: Let A = 2 1 4 so that A4(t) = (t–1)³. Define T : R³ → R³ by T() = Ax. %3D 1 0 3 1 by first (a) Find…

A: Given the matrix A=-10-4214103 so that △At=t-13 and define T:R3→R3 such that Tx=Ax (a) We have to…

Q: 1 0 07 Let A = 0 0 2 0 3 0 %3D Find the Characteristic Polynomial, and compute the Eigenvalues: O…

A: By Bartleby policy I supposed to solve only first one.Post remaining separately again.

Q: Suppose that a 4 x 4 matrix A has eigenvalues ₁-1,A2--2,3-4, and A4--4. Use the following method to…

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Q: 5 3. Consider the matrix A = 45 2. |2 2 2 (a) Find the characteristic polynomial det(A– AI) = 0, and…

A: Given: Consider the matrix A A=542452222

Q: [1 2 8. Let A = and define Q : R² → R by Q(x) = x"Ax. 2 1 (a) Find the characteristic polynomial of…

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Q: For some variable a, let A be the matrix given by -2 A = 3. a 4 -2 (a) Determine the characteristic…

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Q: 6. (a) Let T: L²[0, 2π] → L²[0, 2π] be given by 2п Tf(x) = S cos(xt) f(t) dt. Show that (i) T is…

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Q: p(1) = (1 – 3)(a² + 1 – 6) is the characteristic polynomial of a 3 x 3 matrix A. Then, the…

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Q: Suppose that a 4 x 4 matrix A has eigenvalues A4 = 1, A2 = - 3, A3 = 6, and A4 = - 6. Use the…

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Q: For each of the following matrices (with coefficients in R) compute the characteristic polynomial…

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: Q1 For the given matrix M. Find the Eigen values and their corresponding vectors. sin n/2 2 cos 2n…

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Q: 5.2. The characteristic polynomial of the matrix below is t3-4t 1. Determine the missing entries. 0…

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Q: 2) - Dr. M of the following is the characteristic polynomial of the matrix A = Select one: p(X) = X2…

A: We have to solve

Q: 2x2 Theorem 4d: Suppose A E R has a complex eigenvalue A = a - bi e Cwith b 0 and a complex…

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Q: ) Suppose T E L(V) and T2 = 1 and-1 is not an eigenvalue of T. Prove that T =1. OGive an example of…

A: Hello. Since your question has multiple questions, we will solve first question for you. If you want…