Let A be a 5x5 matrix and let 1 be an eigenvalue of multiplicity 4. If the rank of A-AIis 2, explain why A will, or will not, be defective.

Q: 8 -3 0 7 9 2 -1 0 2 0 0 8 O O

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Q: 201 12 20 -1 0 3

A: We have to find the eigen values of the given Matrix.

Q: Diagonalizing a Matrix In Exercises 7-14, for each matrix A, find (if possible) a nonsingular matrix…

A: The given matrix is A=2-2   30   3-20-1   2 We have to find a nonsingular matrix P such that P-1AP…

Q: Let 1 be an eigenvalue of the n x n matrix A. Let B = A- AI. Show that B is not an invertible…

A: Let A be an n×n matrix. The characteristic polynomial of A is the function f(λ) given by…

Q: Construct an example of a 2x2 matrix with only one distinct eigenvalue.

A: Construct an example of a 2 x 2 matrix with only one distint-eigenvalue

Q: A be an orthogonal n by n real matrix where n is an odd number. Show that 1 or -1 must be an…

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Q: Give an example of a 3x3 matrix with eigenvalues 0,1,2

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Q: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

A: Give an example of a 3x3 non triangular matrix with with eigenvaluse 2,3,-2

Q: 3 2 -3 3 -4 - -2 5]

A: The given matrix is 32-3-3-49-1-25 We have to find  the eigenvalue of the matrix. Then by using the…

Q: : Suppose a 2 x 2 matrix A has 0 as its only eigenvalue. Is A necessarily the zero matrix? If so,…

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Q: Explain why a symmetric matrix with real entries can't have complex eigenvalues.

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Q: Determine all n × n symmetric matrices that have 0 as their only eigenvalue.

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Q: If a square matrix A has two equal rows, why must A have 0 as one of its eigenvalues

A: Given: A is a square matrix having two equal rows.We need to show 0 must be one of the eigenvalues…

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

A: We Construct a 3x3 non-triangular matrix which has three distinct eigenvalues. Determine eigenvalues…

Q: Find the eigenvalues and all possible Jordan forms if A 2 = zero matrix.

A: If A^2 = 0, then the characteristic polynomial of A is λ^2 = 0, which implies that the only…

Q: Give an example of a defective matrix whose rank is not equal to the number of nonzero eigenvalues.

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Q: Write the 4 x 4 elementary matrix which accomplishes the row operation R3 - 5 R2 ---> R3 when you…

A: let  I be the 4×4  identity matrix I=1000010000100001

Q: Prove that the sum of two symmetric positive definite matrices A and B is positive definite (A+B)…

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Q: Give an example of a matrix A with the order 2x2 along with two vectors a and b, with terms a is an…

A: Use simple matrix theory of eigenvalues to come up with this example

Q: -9 4 4 1. Let A = -8 3 4 . Find an invertible matrix P and diagonal matrix D so that A = PDP-1.…

A: See the detailed solution below.

Q: Consider the following matrix A - 4-3 -2 Lnd the eigenValues, eigenvectors

A: 1st we will find Characteristic  polynomial  and then find eigen values by equating it with zero .…

Q: Explain how to find a basis for the eigenspace associated to the eigenvalue -4 in the matrix 4x4…

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Q: Why do the eigenvalues of a triangular matrix lie along its diagonal?

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Q: All 2x2 matrix have 2 different eigenvalues True O False

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Q: If the eigenvalues of a 3×3 matrix A is 1, −2 and 20, what are the eigenvalues of A-1?

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Q: 5.-28 -18 457 29 - λ = λ = 2, (3, 2) 1, (5, 3)

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Q: Determine if v is an eigenvector of the matrix B -47 26 2 B = , v = -78 44 -5

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Q: uppose A is a diagonali= . Would this be true if

A: Given, A is a diagonalizable n x n matrix whose eigenvalues are all 1 or -1.

Q: An nxn matrix is diagonalizable if it has n distinct eigenvalues. O True O False

A: In this question, we have to determine whether the following statement is true or false : "An n×n…

Q: The equation A² - 2A + I = O implies that ---Select--- Need Help? Read It ✓. It follows that…

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Q: If A be nxn matrix with eigen value L then find the eigen value of inverse of A .

A: The given matrix A be an n×n matrix with eigenvalue L. Calculate the eigen value of inverse of A.

Q: Suppose a 3 x 3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A) = -1 and…

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Q: How are the eigenvalues of AH related to the eigenvalues of the square matrix A?

A: Given: The eigenvalues of AH and the eigenvalues of the square matrix A.To find: The relation…

Q: 1 if k = i and l = j if k = j and l = i if k = l but k # i, j 1 (Si3)ke = 1 otherwise.

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Q: Give an example of a 3 x 3 matrix with eigenvalues of 2, 2, and -3 that is NOT diagonalizable. Show…

A: Consider the matrix 21202100-3 Since the given matrix is in upper triangular form , so the eigen…

Q: let Ax=b where A is n*n matrix and b = [bi]. find out the number if multiplications additions and…

A: Given: The equation is Ax=b where A is a matrix of order n×n and b=bi. To find: the number of…