13. If the characteristic polynomial of a matrix A is * p(2) = 23 - 22- 62. Then tr(A) = %3D %3D O -6 O 5 ONone

Q: Find the characteristic polynomial of the matrix 5 A 0 -5 -1 -4

A: Characteristic polynomial is obtained using the expression |A-λI|, where I is the identity matrix.

Q: (b) Find the characteristic equation of the matrix P defined by [2 1 1] P = 1 2 1 li 1 2] Further…

A: The given matrix is P=211121112 the characteristic equation is given by P-λI=02-λ1112-λ1112-λ=0…

Q: a) If a 7 × 5 Matrix A has rank 2, find dim(Null A), dim (Row A) and rank AT

A: 1) Given  7×5 matrix  rank(A)=2 using rank nullity theorem we have rank A + null A= number of…

Q: Find the characteristic equation of the matrix by inspection. 4 2] -6 0 0 6 0 0 5] 4 -9 LO

A:

Q: Suppose A = 3 9 1 Find an invertible matrix P and a diagonal matrix D so that A = PDP-'. Use your…

A:

Q: [2.25] Show that C= {x : Ax <0}, where A is an m × n matrix, has at most one extreme point, the…

A: 2.25)   show that C=x:Ax≤0 where A is an m×n matrix , has at most one extreme point, the origin.…

Q: 4. Give an example of an indefinite quadratic form on R³ whose corresponding symmetric matrix has no…

A: Let Q(x1,x2,x3)=-x12-2x1x2+6x1x2+3x22-2x2x3-x32 be a quadratic form whose symmetric matrix is…

Q: Find a matrix A such that e [-] -2 is a solution for Ax= x'.

A:

Q: [3 Compute the natrix exponential e4t for the diagonal matrix A = !!

A:

Q: 2. Find the general solution of the system of differen- tial equations d '( cos(3t) - sin(3t) 9 3…

A: Given that the characteristic polynomial of A=93-39 is λ-92+32. The eigenvalues of A are the…

Q: At Compute the matrix exponential e for the system x' = Ax given below. x₁ = 37x₁ - 36x₂, x 2 = 34x₁…

A:

Q: If A is an m · n matrix where A· A is defined, and k e N, recursively define A*

A: If A is a m × n matrix where A • A is defined and k lies in N then we have to recursively define Ak…

Q: 6. Suppose  X + XB = C, where X, B, and C are square matrices of the same size. a.  Derive an…

A: We will see that (I+B) must be invertible for existence of X.

Q: 9. Suppose that M is a 2 × 2 matrix over R, with characteristic polynomial det(AI – M) = X² – 21 + 3…

A:

Q: 2) An n x n matrix A is called nilpotent if Ak = 0 for some positive integer k. Show that if A + 0…

A:

Q: highlighted" condition. A matrix in M2(R) which is “nilpotent" and has a non-zero entry in each row…

A: A matrix is Nilpotent if Ak = 0 where 0 is null matrix and k is index of matrix A.

Q: 2 1 -1 4 previous problem to determine a matrix S such that Show that A is defective and use the 3…

A:

Q: 3. Let A [1.1 -0.1] [0.3 0.7 0.7] Is matrix A invertible? How do you know?

A: An invertible matric is a matrix  for which matrix inversion operation exists . A matrix is said to…

Q: 5. Compute the condition number K(A) of the following matrix 1 1+€ 1 1 1 A 1 1 1 1+€ What is k(A) as…

A: Conditional number is κ∞(A)=∥A∥∞·∥A-1∥∞.If matrix A is known to us so ∥A∥∞ is easy to find .First…

Q: Solve the initial value problem for the linear system æ' = Ax in dimension 3, where -1 -1 A = |1 5…

A:

Q: .1 Suppose A is a matrix with characteristic polynomial CA(x) = x²(x – 1)³(x+2)². Determine the…

A: The solution are next step

Q: determine whether the given matrix is defective or nondefective.

A:

Q: 4 9- That is, find an -5. | Diagonalize the matrix A [3 invertible matrix P and a diagonal matrix D…

A: Given matrix A=4-63-5

Q: a) suppose A is a 3x3 matrix with the characteristic polynomial pld) = -d? (At3), If A is…

A: Given, matrix A is diagonalizableand characteristics polynomial of Ap(λ)=-λ2(λ+3)We can find…

Q: Show that the characteristic equation of a 2 × 2 matrix A can be expressed as 1² – tr(A)A + det(A) =…

A:

Q: 4. Suppose A is a nonsingular matrix with SVD A= UEV*.

A:

Q: Find the singular value decompostion of the matrix. 1 1 -1 -1 1

A:

Q: Consider A = 21 2 1 3 -1 -3 4 Convert A to an upper triangular matrix U by using Gaussian…

A:

Q: (1) Suppose the last column of AB consists of all O's but B itself has no column of zeros. Are the…

A: as you are asking multiple questions I have solved first one , please repost with the remaining…

Q: 3. Find that whether the following matrix is singular or nonsingular. 8- 01 0 - 0 -5] 0 - O 0

A: Singular and Non-singular matrix- Let A be a square matrix, such that the determinant of A is…

Q: : Show that there are no nxn matrices A and B such that AB – BA= In. & You may cite, without…

A:

Q: 2.2.8 Show that if a matrix is positive definite then it is invertible, and its inverse is also…

A:

Q: Q3. In the triangular decomposition of a symmetric nxn matrix (in the form of LL"), the number of…

A:

Q: prior to Exercises 15–18 in Section 3.1. [Note: Finding the characteristic polynomial of a 3 x 3…

A: The characteristic equation to the matrix can be obtained using the formula A-λI=0. The determinant…

Q: Suppose that A is an n × n matrix and det A + 0. Determine the rank and nullity of A.

A:

Q: Find a 2 x 2 matrix A with integer entries where the characteristic polynomial |A – AI| is X² + 2A +…

A: Finding such a is equivalent to finding a 2 by 2 matrix with trace -2 and determinant 5. As in…

Q: Find the characteristic polynomial of the matrix 2 A : 4 -4 -4 p(x) =

A:

Q: Find the Jordanm Canonical form of the matrix A which has the charactwristic polynomial is and…

A: Solve the following

Q: Find the characteristic polynomial of the matrix 1 3 A = -1 -4 -4 4 p(æ) =

A: Where we have to find out the characteristic polynomial of a given matrix

Q: Let A be a 4 × 4 matrix and suppose that A is a diagonalizable. If the characteristic polynomial of…

A:

Q: If A? is a zero matrix, then AT A = 0 is: %3D O a. Not possible unless A is a zero matrix O b. not…

A:

Q: 3.1.Let a matrix B is B = FindB6 by using anonsingularmatrix P suchthatD = P¯-"BP is diagonal.

A: We are given: B = 2213 We need to find out B6 using P-1BP. This can be done as follows:

Q: 15 2 Suppose that G- is the Leslie Matrix of a population with two age groups. a (a) For which value…

A:

Q: 5. Identify an elementary matrix E such that 1. E- 2 2 4.

A:

Q: 2.12. Let a non-zero matrix A satisfy A° = 0. Prove that A cannot be diagonalized. More generally,…

A: To prove that A can't be diagonalised

Q: In matrix notation it can be shown that ß = (X'X)-'X'y What happens to ß when there is perfect…

A: i) Perfect collinearity among X' s means there is strong or significant relationship among the…

Q: 3 5. Suppose that A is an invertible matrix with A-1 a. Find A.

A:

Q: Show that A and B are not similar matrices. 2 1 , В 3 3 -1 A = -3 7 -6 Since A has characteristic…

A: