Let A be the following matrix 4 5 3 6 4 8 2 4 3 After diagonalization, Pand Dare found such that A = PDP !Find the trace of D.

Q: 1. Calculate exp(A) where A is the 2×2 matrix given by A 7 -2 -[33] = 5 5

A:

Q: 3. Let 1 B -1 Consider T : R²,2 → R²2 defined by T(A) = AB – BA. Let - 이 [0 [o o] [o o] [1 0] Bị and…

A:

Q: If A and B are similar, then there exists a matrix P such that B = PAP. Use this fact to fi -2 2 -3…

A: Here we have to find B5 ,   We have to find if A and B are similar or not, if A and B are similar…

Q: For A 3 1 N² = A. 2 find a 3 x 3 matrix X such that

A:

Q: Let A = [ 9-8 4-3 Find an invertible matrix X such that X-¹AX is diagonal.

A: Introduction: A matrix A of dimension n x n is called invertible if and only if there exists…

Q: Let 0 9. A = = [6 0 Is it possible to find a two by two real matrix B such that A = eB₂

A:

Q: Let A be an n xn matrix andB=A+1, where / is the identity matrix, then it is possible for A and B to…

A: False

Q: Let A and B be similar matrices Show that if A? = A then B = B.

A: Two matrices C and D are said to be similar matrices if there exists a non-singular matrix P such…

Q: Let A be the following matrix: A = Find the scalar multiple –5A: 0 -3 2 3

A: The given problem is to find the scaler multiple of the given following matrix of A. Scalar multiple…

Q: Let A, B, C be nxn matrices. If B = CAC- show that det(A) = det(B).

A: Given that A,B,C be n×n matrices. Also  B=CAC-1 To Prove: det(A)=det(B) To prove the result we…

Q: = 1 -2 2 00 0 -1 0 0 -1

A: Given that A=

Q: Let A be a square matrix such that A = 0. Show that 4 : (I – A)-1 = I+ A+ A? + A³. Here I is the…

A:

Q: Find an SVD of the matrix. A=

A:

Q: Find ATA for the matrix. Show that this product is symmetric.

A: The transpose of matrix A is,

Q: Let A and B be square matrices. If AB is nonsingular, prove that both A and B are nonsingular.

A:

Q: 2. Find a real 2 × 2 matrix A (other than A =I) such that Aº = I . %3D

A:

Q: Find the LU factorization of the following matrix: 203 1 3 1 01 1

A:

Q: 3 2 A0 -1 A 1 3 A 0 -2 5

A:

Q: Consider the matrix A 1 2 11 A = |1 5 0 [3 0 5/ Find the adjoint of A. b. Find the inverse of A. а.

A: