7. Let A be an 12 x 12 matrix given by 2 1 2 A = 1 2 1 2 -3 3 1 3 5 01 (a) What are the eigenvalues of A? (b) What are algebraic and geometric multiplicities for each of the eigenvalues? (c) What is the characteristic polynomial of A? (d) What is trace(A)? What is det(A)? What is rank(A)?

Q: Please explain step by step how to do parts a, b ,c with the solution

A: Step 1: (a) To find the characteristic polynomial of matrix  A , we compute  det(A−λI), where λ is…

Q: Trace of the matrix =Sum of the Eigen values  True  False

A: Trace is sum of diagonal elements with also equals sum of eigen values.

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Q: 7. (Review) Determine the characteristic polynomial, the eigenvalues, a basis for the eigenspace,…

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A: A=00-2121103

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Q: A = |I

A: Note: Here we solve first 3) subpart for remining question submit it again with mentioning the…

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Q: Do (a), (b) and (c) for the quadratic forms in 1.1 and 1.2: (a) Make a change-of-variable…

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Q: 24. Consider the quadratic form Q(x) = -x² - 2y² - z² + 2xy - 2yz a) Find a symmetric matrix A such…

A: As you asked more than 3 sub parts , so I solve first three sub part , please  repost the remaining…

Q: 4 2 ind the Eigen values of the matrix A = |-5 3 2

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Q: Advanced Math Question

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Q: -1 Let be the eigenvector corresponding to the largest eigenvalue of the matrix 1 -1 x A =0 -1 2 2…

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Q: e State the Spectral Theorem for real-valued matrices.

A: According to guidelines we can do only first question thank you We have to give the Statement of…

Q: (5) Let E be the matrix 0 -3] -2 2 3 E = 4 1 7 (5a) Find all of the eigenvalues of E and a basis of…

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Q: 2. The eigenvalues 31 Let A =-2 6 4 2 and corresponding eigenspaces are: -1 2 = 7: 1 and 1 = -2: 1/2…

A: Given,

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A: 4.The given matrix,.The objective is to find the characteristic polynomial, eigenvalues, and…

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Q: (3 5) 5. Let A 2 6 (a) Find the characteristic polynomial of A. (b) Find the eigenvalues of A.

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Q: Let A be a 6xó matrix with the characteristic equation 1?(1 - 7)(A - 12)3 What are the possible…

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Q: Part: b:Diagonalize the following matrix if possible whose eigenvalues are given to be 0, 1, 1. -1…

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Q: -4 2 Given the matrix 4 the eigenvector is 3 8 (b)

A: Introduction :