A) Find the eigenbasis of the matrix and diagonalize it (if possible): when p=4. Also, Use this diagonalization to find A^3 and A^7. (the matrix in the photo)    B) For the matrix in part (A), find A^2 and A^1 theorem.using Cayley-Hamilton

Q: Find an LU factorization for the matrix A = -2 3 4 1 -3 0 2 3-2, Verify that LU = A.

A:

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

A:

Q: a) For invertible matrices A, BER"Xn, show that ((AB)")- = (A-)"(B)".

A:

Q: 4 -5 -9] 0 -3 1 -2 -3 The matrix A has an eigenvalue A = -3. 1

A:

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: A is an n × n matrix with the property that A^2 = A. (a) If B = In − A, show that B^2 = B. (b) Show…

A:

Q: Consider the linear system ² - [ 8 - 1] = = x. 6 Find the eigenvalues and eigenvectors for the…

A:

Q: Find the eigenvalues and eigenfactor for the two by two matrix [0,1;-2,1]

A: Step 1:Step 2: Step 3:

Q: Derive a composite matrix that transforms a square ABCD with coordinates A(0,0), B(1,0), C(1,1),…

A: As per the question we have to find the affine transform which will transform the points A,B,C,D…

Q: A = -53 -70 35 45

A:

Q: Let (x, y, z) E R³ and the transformation T: R³ → R² be given by T(x, y, z) = (2x + 4y, x + 3y + z).

A:

Q: Create a world transform matrix that translates by 3, 5, 7 and rotates 80° about the x-axis.

A: Detailed explanation mentioned below

Q: a) For invertible matrices A, BE R™×", show that ((AB)")-1 = (A-1)" (B1)". b) Let A, B, C, D e R"*"…

A:

Q: Get a base for the column space of the matrix shown in the image

A:

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

A:

Q: Find a 2 by 2  matrix that scales the point (x,y) by 0.5 in the x direction and 3 in the y…

A:

Q: solve the last question from the picture above, #5 eigenvalues ,2,,3,4,5 if the matrix is…

A: for ease of everything I will provide whole answer.

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

A:

Q: For the matrix below, find the associated eigenvalues. 여름 리 Problem C=

A:

Q: 1. Show that the following functions are convex by verifying the definition, i.e., that f(x +…

A:

Q: Find a real matrix A such that A ^6 = (09, -90)

A:

Q: t A be the square matrix (abcd) A. If ad−bc = 1, then show that A^−1 =(d−b−ca ) B. If ad−bc=α, then…

A: If  is a square matrix then its inverse is where

Q: Find the Eigenvalue(s) of the matrix Row 1: (-2,0,0,0) Row 2: (35,6,0,0) Row 3: (?,-12,4,0) Row 4:…

A: (.)  Let the matrix  is ,            A =  -200      03560      0*-124       08*0 -2 where  * are…

Q: Let a and b be real numbers. Find the eigenvalues and corresponding eigenspaces of matrix over the…

A:

Q: (a) Find all eigenvalues of the matrix 2 -10 8 A =0 -2 4 %3D -2 (b) Find the eigenvectors of the…

A:

Q: 即 -2 0 1 E). EL 0 亦 2 心→ I I - 一1

A:

Q: 4. Find the symmetric matrix, diagonal form of the quadratic form Q = 2x2 + 2y2 + 2z2-2xy-2xz- 2yz,…

A: We have to find the quadratic form of the equation Q=2x2+2y2+2z2-2xy-2xz-2yz which is a polynomial…

Q: Use matrix multiplication to find the contraction of (a,b) with factor k =1 / alpha, where alpha is…

A:

Q: Let B=[0000]. Find a non-zero 2×2 matrix A such that A^2=B. A= ? Hint: Let �=[����] and then set…

A: The given matrix is; B=[0 0      0 0 ]A2=BFind the matrix A.

Q: 5 -1 0 -5 9 5 -1 0,

A:

Q: tion # 2: b:Diagonalize the following matrix if possible whose eigenvalues are giv 0 -1 -1] A = 1 2…

A:

Q: 3by3 matrix A with eigenvalues lambda1, lambda2 and lambda3. What will be the eigenvalues of inverse…

A:

Q: -37 -1 0 -1 4 0 -1 -1 4 -1 0 A = 3

A: Here we use the gram Schmidt process to find the QR decomposition of matrix

Q: Let A be a 2 x 2 matrix a If ad – bc + 0, then A-1 ad-be ad-be ad-e ad-be. such that [1 AA-1 = A-'A…

A:

Q: Explain how to determine whether any matrix A is Diagonalizable using (a). Eigen vectors , (b).…

A: To check whether a Matrix is Diagonalizable following statements may  be used

Q: To divide the LHS by a matrix on the RHS, what steps do you follow?

A: To find: To divide the LHS by a matrix on the RHS, what steps do you follow?

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: Rotate the quadratic function 5x^2 + 3y^2 + 2z^2 + 4xz = 14 to its principal axes and express this…

A: