1. Let A = 1 2 4 1 0 0 0-1 3 Answer the following a. Find the characteristic polynomial of A, and use it to find the eigenvalues. b. Find a basis for each eigenspace. c. Use your answer to diagonalize A as PDP-¹. Do not find P-1, instead verify by showing that AP = PD.

Q: List the eigenvalues of A. The transformation x--Ax is the composition of a rotation and a scaling.…

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Q: Q1.B. if k-1 is an eigen value of (₁2). find one corresponding eigen vector?

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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: Find the basic eigenvectors of A corresponding to the eigenvalue 2. -1 0 8 4 1 0 -8 -4 2 = -1 4 A =…

A: Given:  A=-108410-8-4-209440-16-7,λ=-1

Q: and $.f What are the eigenvalues eigenvectors of A = [= 1 ² ] *²² 2 √56 = √√2.2² 53 - b ± √b²2²4₁c…

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Q: Find a basis for the eigenspace corresponding to the eigenvalue. A = 622 2 94,λ=5 -2 -4 1

A: Given matrix:- A=622294-2-41

Q: -2 -4 2 -2 2 4 2 5 1.

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Q: ] 1. Use the characteristic polynomial to find the eigenvalues of A. Call them X₁ and X2. Consider…

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Q: Find all values of the angle 0 (in radians, with 0 < 0 < 2n) for which the matrix cos e -sin e sin e…

A: Since you are asking multiple questions. We are answering only the first question as per our…

Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

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Q: Let A = | -4 8 10 8 3 7 a) Find the characteristic polynomial of A. b) Find all the eigenvalues of…

A: The matrix is A=600-4810837. a) The characteristic polynomial  is obtained using the equation…

Q: 2. In this course you mainly work with matrices that have real eigenvalues. But, what about the…

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

A: λ=1 is the eigen value of A=5412

Q: Calculate the characteristic polynomial of the following matrix A, and use it to compute eigenvalues…

A: We have to find the characteristics polynomial and eigen values

Q: 2. Show how to find the characteristic polynomial det (A-XI) and how to use it to find the…

A: A=1331

Q: Let A be a diagonalizable 3x3 mat rix with P AP = -I,where I is the identity mat rix. Which of the…

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Q: Consider the function T : P2(R) → P2(R) given by T(a+ bx + cx²) = (a – b+ c) + bx + (-b+2c)x² Find…

A: Firstly we will find matrix associated with T.

Q: 1. Answer the following for A = -3 -5 -3 3 3 1 a. Determine the characteristic polynomial of A and…

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Q: 6. M = 2 -7 1-6 a. Find the characteristic polynomial and eigenvalues of M. b. Find a basis for the…

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Q: List the eig composition of a rotation and a scaling. Give the angle o of the rotation, where - =…

A: please comment if you need any clarification. if you find my answer useful please put thumbs up.

Q: Let A=[5 2; 2 8] a. Show that A is positive definite

A: a A=5228we find the eigen value of matrix A ⇒5228-λ1001=5228-λ00λ=5-λ228-λ

Q: 3. Find the eigenvalues and cigenspaces, as well as a basis for each eigenspace. (a) [88] 12 3 4 000…

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Q: Let p(λ) be the characteristic polynomial of the 4 × 4 ma- trix A. Using algebra, you compute the…

A: Given that A is a matrix of order 4×4 and λ be the eigen value,Then characteristic equation is given…

Q: ind the eigenvalues of A, B. and C: 1 2 3 A =0 4 5 0 0 6 and B =0 2 0 3 00 目 2 2 2 2 2 2 2 2 2 and C…

A: Eigen value of matrix A is 1,4,6. Eigen value of matrix B is 2, -√3, √3.

Q: 1. Answer the following for A = b. Find a basis for the eigenspaces. 1 -3 3 3 3 -5 -3 3 1 ننا ننا

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Q: decide if the given statement is true or false,and give a brief justification for your answer. If…

A: Eigenvalue: A number λ is said to be an eigenvalue of a matrix A if there exists a non-zero vector v…