3. Suppose that the characteristic polynomial of a square matrix A is fA(^) = –X³ + 3A (a) What is the size of A? (b) What are the eigenvalues of A? (c) What is tr(A)? (d) Is A invertible? Why or why not? Is A diagonalizable? If so, determine a diagonal matrix that is similar to A. (e) If not, explain why not.

Q: Find the eigenvalues of A and B (easy for triangular matrices) and A+ B: A - B [3 ]-[ 1 1 : λι λι ³…

A: If A is any matrix.λ is an Eigen value of A if det(λI -A) =0Where I is identity matrix.  Given,…

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A: We find characteristic polynomial and eigenvalues of A.

Q: 10. It is known that matrix A 4x4 has the following eigenvalues: 2, =-2, 2, = 1, z =-1, 24 = 2.…

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Q: 21.1f A' = 34² where A is n by n matrix, then (a) A= 31 (b) A 31 if rank((A) =n () A" =!1 (d) a and…

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Q: For the matrix A, find (if possible) a nonsingular matrix P such that P-'AP is diagonal. (If not…

A: We have to diagnolize the matrix A.

Q: - find the eigenvectors of the diagonal matrix (Â) J where. 2 5 0-12 2 4 10 A = and P=["} 1 2 5 4 O…

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Q: ^-1 13. (a) Find all eigenvalues and corresponding eigenvectors of A = (b) Explain how you can…

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Q: For the following matrix [40 0 0 0 2 0 0 00-1 0 Loo 0 -2. In your answer, use 3 significant digits…

A: Please see the below picture for detailed solution.

Q: (e)  Show that the matrix is diagonalizable and find an invertible matrix P and a diagonal matrix D…

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Q: Diaganolize the following matrix such that: D=(P^T)(A)(P). Rather than finding the inverse matrix,…

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Q: 4) (a) The matrix A is factored in the form PDP!. Use diagonalization theorem to find the eigen…

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Q: f A be a square matrix given by 300 02-5 then find all the 0 1 -2 eigenvalues of A viewed as…

A: Provided  the matrix is                   A=30002-501-2    our aim is to find the eigen values of…

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Q: Let A be 2 x 2 matrix with trace(A) = 5 and det(A) = what is the value of 4X₁ +8X₂ ? tr(A) = = 5 ve…

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Q: Let A= (in the picture) (a) Find the eigenvalues and eigenvectors of A. (b) Rewrite A in the form A…

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Q: 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…

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Q: i had a typo can you also find the eigenspace for the given matrix

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Q: Find the characterstic polynomial of A Using your answer to part (a), check that X₁ A. What are…

A: Please note that as per bartleby guidelines, I can answer only one question.

Q: c) If A is a 5 x 4 matrix, what is the largest possible dimension of the row space of A? If A is a 4…

A: Q1.c  A  is  a 5×4 matrix   A=a11a12a13a14a21a22a23a24a31a32a33a34a41a42a43a44a51a52a53a54 Row space…

Q: ) Construct a 3x3 non-triangular matrix, which has three distinct eigenvalues. Determine eigenvalues…

A: For example: Let            A=5-10-15000-2

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Q: 3) Find a sequence of elementary matrices whose product is A and a sequence whose product is A'. - 3…

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A: The values are:-

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Q: Solve the following equations by Cramer's Method:- 3 x - 5y = 4 and x - y = 4 ASAP!!! PLEASE

A: The equations can be expressed as 3x - 5y - 4 = 0x - y - 4 = 0