3. If A = 1,1 = 2, and 1 = 3 are3 eigenvalues for an nxn matrix A, what can you say %3D about n, the size of A. Will A be diagonalizable? Explain.

Q: If λ is an eigenvalue of a matrix A, prove that λ3−5λ is an eigenvalue of the matrix A3−5A

A: Given: eigen value of a matrix A is λ. By definition of eigen value Ax=λx…

Q: Let 4 1 A = | 2 3 2 1 0 4 (a) Find the eigenvalues of A. (b) For each eigenvalue 2, find the rank of…

A: Given matrix is 401232104. a We have to find the eigenvalues of A. The eigenvalues of A are the…

Q: 14. Find a 3 x 3 matrix A that has eigenvalues A = 27, 45, and -9 with corresponding %3D…

A:

Q: If A is a 3 x 3 matrix such that A' = - A, then 0 is an eigenvalue of A %3D Select one: True False

A:

Q: 31. Show that if A is an eigenvalue of a matrix A, then A2 is an eigenvalue of A?.

A:

Q: Give an example of an m x n matrix A such that the nonzero eigenvalues of A'A are distinct from…

A: We have to solve given problem:

Q: 26. Show that if A² is the zero matrix, then the only eigenvalue of A is 0.

A:

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

A:

Q: Determine if the following statement is true or false, and explain why: If an n x n matrix is…

A:

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

A:

Q: If A is a 5 × 5 real matrix with trace 15 and if 2 and 3 are eigenvalues of A, each with algeraic…

A: Solution: Given  A is 5×5 real matrix  and trace(A)=15  and we have to find det(A)

Q: If A is 3 x3 matrix with eigenvalues A= 4,4,3 , then A is defective. Select one: O True O False

A: We have given a matrix A . A is 3×3  Eigenvalues λ= 4,4,3. Here λ=4 is eigenvalue of multiplicity 2.…

Q: Suppose that E is a 4 x 4 matrix in which every row sums to the constant k. Explain why u =…

A:

Q: Let A be a 5 × 5 matrix with 3 eigenvalues

A:

Q: 3) Is it true that an eigenvector of A is also an eigenvalue of A² for a square matrix A?

A:

Q: 14. Assume that a matrix A has only zero eigenvalues. What is the Jordan-Normal Form of A? What is…

A: Given that matrix A has only zero eigenvalues. Jordan's normal form of A and the main diagonal of…

Q: Let A be a 5 × 5 nonsymmetric matrix with rankequal to 3, let B = ATA, and let C = eB. What, if…

A:

Q: 3. In each of the following cases, is it possible for A to have no real eigenvalues? If yes, give an…

A: The solution are next step

Q: If A is 3 x 3 matrix with eigenvalues A= 4,4,3 , then A is defective. Select one: O True False

A:

Q: Show that A = 3 is an eigenvalue for the following matrix, and find one eigenvector. (3 1 A = |0 1…

A: Eigenvalues of a matrix A are given by the equation detA-λI=0. Here det represents determinant and…

Q: 6. By using the power method, the smallest eigenvalue A of the nonsingular matrix B equal to…

A: Answer is 'False'.

Q: If the eigenvalues of a 3×3 matrix ? is 1, −8 and 50, then the eigenvalues of ?T are 1, −8 and 50.…

A:

Q: Find the matrix A of the quadratic form assoe 2x2 - 3xy - 2y2 + 11 = 0 A = Find the eigenvalues of…

A:

Q: Find the largest eigenvalue of the following matrix: [1 1 A = 8 1 #Give your answer to 2 decimal…

A: The given matrix is                               A=1181 The characteristic  equation of A is…

Q: If the eigenvalues of a 3×3 matrix A is 1, −8 and 50, then the eigenvalues of AT are 1, −8 and 50.…

A:

Q: For which value of k does the matrix A=[2   k]     [−4 5]   have one real eigenvalue of…

A:

Q: 2. Determine whether there exists a 3 x 3 symmetric matrix whose eigenvalues are A1 = -1, A2=3, A3 =…

A:

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

A:

Q: If A ER is a common eigenvalue of two n x n matrices A and B, then A is also an eigenvalue of A+ B.

A:

Q: 2. Determine whether there exists a 3 x 3 symmetric matrix whose eigenvalues are A1 = -1, 2= 3, A3 =…

A: Introduction: A diagonal matrix is one that only has non-zero values on its major diagonal. To put…

Q: 9. Let 1] A = 2 |1 0 4 3 2 a. Find the eigenvalues of A. b. For each eigenvalue 2, find the rank of…

A: Using matrix function

Q: If A is 3x3 matrix with eigenvalues A = 4,4,3 , then A is defective. Select one: O True O False

A: If A is 3×3 matrix . The eigenvalues are given as λ=4, 4, 3. Since the eigenvalues of the matrix A…

Q: A=

A: The given matrix,  A=8k6-6

Q: Consider the given matrix. 3 0 0 0 2 0 12 0 1 Find the eigenvalues. (Enter yo

A:

Q: If A is a 3 × 3 matrix which has eigenvalues 2 = 10, 1 = -2, and 2 = -3. Then A is diagonalizable…

A:

Q: The lower bound for the eigenvalue of the 2 -1 2 -4 -1 2 1 3 is 2 1-1 0 matrix A = -4 3 0 4 a.-4 b.…

A:

Q: Find the 2 x 2 matrix A that has the eigenvalues and eigenvectors (6) . 6) A1 =1 = A2 = -1

A:

Q: If A is a (real) square matrix and v is an eigenvector for A with length ||1|| = 4 %3D and…

A: As A is a square (real) matrix and v is an eigen vector for A corresponding to the eigen value λ…

Q: Show that if 1 = 4 is an eigenvalue of an n × n matrix T, then 16 is an eigen- value of the matrix…

A:

Q: If A is 3x3 matrix with eigenvalues A=4,4,3, then A is defective. Select one: O True O False

A:

Q: If A is a 4 x 4 matrix such that 3 is the only eigenvalue of A, then the characteristic polyn of A…

A: Solution of the problem as follows

Q: 6. Consider the matrix A Compute the eigenvalues of A, and the corresponding eigenspaces.

A: Given matrix is A=1153. We have to find the eigenvalues of matrix A and the eigenspace corresponding…

Q: If A is 3 x3 matrix with eigenvalues A = 4,4,3 , then A is defective. Select one: C True False

A: If A is 3 × 3 matrix with eigenvalues λ = 4, 4, 3  Then,  A is defective  We have to tell it is true…

Q: 4. Find the eigenvalue and eigenvector of the matrix: 20 -2 0 4 -2 0 O 5.

A:

Q: For which value of k does the matrix 4. A = 6 2 have one real eigenvalue of multiplicity 2?

A:

Q: Consider the following matrix A (whose 2nd and 3rd rows are not given), and vector x. 2 2 A = -7…

A: given               A=1   2   1*   *    * *   *    *    x=   2-7  8     Let λ be corresponding…

Q: For which value of k does the matrix 4 k A have one real eigenvalue of multiplicity 2?

A:

Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.