Solve the following exercises, you will need to show all your work to receive full credit. Consider the matrix, 1 3 Knowing that f (t) = (t – 1)²(t – 2) is the characteristic polynomial, do the following: 1. find a basis of eigenvectors; 2. Find P such that P-AP is a diagonal matrix D. Give D

Q: - ; Let A be a square matrix such that A? – 7A+ 81 = 0 (where I and 0 are the identity and zero…

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Q: Q4: Using Cayley - Hamilton theorem to find the inverse of the matrix A, where 1 1 2 A = 3 1 1 2 3 1

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Q: 3(4) 5 A = %3D -1 2

A: Here in the given question find the canonical form of the matrix A, which is P-1 A P = B   Find the…

Q: [x__3y] [x_2y_ 9. Find the inverse of the matrix:

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Q: For the matix A given below, calculate (A-I)T (where I is the 3 x 3 identity matrix). A = 2 -1 0 5…

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Q: Let A = -5 6 -2 3 -11 14 and define T: R² → R² by T(7) = Az. Find T 5. Find 7 ([^;])-4-[-'₁). = A.

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Q: 2. For the matrix 2 2 -1 B -3 3 find its Pseduoinverse Bt and the 2-norm ||B*||2.

A: Given : B=212-1-1-3-13 To find : pseudoinverse B+ and the 2-norm ∥B+∥2

Q: Let A be a 3x3 symmetric matrix. Assume that A has three eigenvalues: A₁ = -1, A₂ = 2, and A3 = 5.…

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Q: 5. For each linear operator T on V, find the eigenvalues of T and an ordered basis for V such that…

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Q: Find the triangular factorization A = LU for the matrix          2  4  -6  A=    1  5  3         1…

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Q: Use the following matrices to perform the operation, if possible. (If not possible, enter IMPOSSIBLE…

A: C=9101D=2653

Q: Find the RREF of the matrix 2 3 12 -2 22 -2

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Q: 2 -1 . Let A -2 3 (a) Find the eigenvalues and corresponding eigenvectors of A. (b) Find a…

A: Given  A=2-1-23

Q: Q1.B. if k-1 is an eigen value of

A: λ=1 is the eigen value of A=5412

Q: 5. For each linear operator T on V, find the eigenvalues of T and an ordered basis for V such that…

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Q: 5. Let T: R R3 be defined by -> X1 + 2x2 X1 T %3D a. Find the matrix [T]B.B relative to the bases B…

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Q: A [11 -2] 50-5 Find the eigenvectors of the given matrix: 181-18) 12 i

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Q: Let v1 = (1,−1,1),v2 = (2,1,3), and v3 = (−1,−1,2) be eigenvectors of the matrix A corresponding to…

A: We know that a number λ is called an eigenvalue of the matrix A if there is a non-zero vector x such…

Q: Find a matrix P such that P'AP orthogonally diagonalizes A. Verify that PTAP gives the proper…

A: For any square matrix , if the matrix orthogonally diagonalizes matrix , then column of matrix…

Q: 3-18. Show that the matrix 2 1 1 1 3 2 13 is a root of the polynomial p(x) = x& – 5x² – 5; that is,…

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Q: X = - 1 1. Construct a matrix that have an A above with multiplicity of 3. 2. Find the eigenvectors…

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Q: X = - 3 1. Construct a matrix that have an A above with multiplicity of 3. 2. Find the eigenvectors…

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Q: +i) is unitary and find A. Prove that the matrix A =

A: Given: A = 121+i12-1+i121+i121-i To do: Prove that A is unitary. Find A-1.

Q: [101] Find the inverse of the matrix C = 0 1 1 using cofactors. Show all your work. L2 1 4]

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Q: a. Solve the following system of linear equations by Gauss Jordan method x +y = 3 3x + 2y = 7

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Q: 1. (C"B)A" 3 A = -1 B = -1 4 C = 1 2. tr(4ET – D) 1 1 1 2 6. 1 3 D = -1 1 E = -1 1 3 2 4 4. 3

A: To evaluate the given matrices.

Q: A = G I 1 1 Find the matrices P and D that orthogonally diagonalize the matrix A such that A = PDPT

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Q: Give an example of a non-zero 2 × 2 matrix R which satisfics R² = 0. Suppose that M is an n x n…

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Q: 1 2 1. Find the inverse of the matrix A = 2 1 4 4 5 10

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