= Given: A is a symmetric 3 x 3 matrix with eigenvalues 1 and 4 and corresponding eigenspaces E₁ Span {[+])} and E4 = Span Find an orthogonal diagonalization for A. {[H]} 1

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: The given matrix is A=1-2-36. To Find: cond1(A ) and cond∞(A) for the above matrix. To Check:…

Q: .

A: Given: Let λ be an eigenvalue of an n×n matrix A. To Show: For some index j, λ-ajj≤∑i≠jnaij (column…

Q: How many of the following are true? Let I. A be a matrix of type nxn as the real variable. If c is…

A: as per our guidelines we are supposed to answer only 3 sub-parts (if there are multiple subparts…

Q: Let A be an n x n matrix, and suppose that the only eigenvalues of A are 0, 1, and 2. (a) Prove that…

A:

Q: Consider the operator R2 → R2 given by left-multiplication by the matrix: A =[−2 −1,        1 −4].…

A:

Q: , a linear operator and a scalar λ are given. Show that is an eigenvalue of the operator and…

A: Given linear transformation…

Q: For the following matrices A, compute AT. If A is a 2x2 matrix with real, different eigenvalues,…

A:

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: We first need to find the inverse of the matrix.

Q: 5. Let A be an n x n matrix. Show that any collection of eigenvectors of A corresponding to…

A: Let A be a n × n matrix then we have to prove that eigenvectors corresponding to different…

Q: - Lat A = - 2 - 2 3. 2. 1- - 2 11

A:

Q: Find the characteristic polynomial and all eigenvalues and eigenvectors for each matrix. Use those…

A: Given the matrix is  d -45-5-4e -25302-40-12f 05-22

Q: .

A:

Q: Find the characteristic polynomial and all eigenvalues and eigenvectors for each matrix. Use those…

A: We find the eigen value and eigen vector the above matrix

Q: Let A = [2] and C = [12] and X be the 2 x 2 matrix satisfying AX-2C = 31₂. Then a. X = NINMIY HIM b.…

A:

Q: Suppose A is a 2 x 2 matrix. Show that the constant term of the characteristic equation |A – XI| = 0…

A: According to the given data, shows that the constant term of characteristic equation is equal to…

Q: and the vector u = Consider the matrix A = and 22 So u is an eigenvector with corresponding…

A:

Q: How many of the following are true? Let I. A be a matrix of type nxn as the real variable. If c is…

A:

Q: For each of linear transformation T given below, do the following: (i) finc of T, (ii) find each…

A:

Q: Find x such that the matrix is singular. 4 X A -2-6 X3D

A: Given Matrix is, A=4x-2-6 we know that, A matrix is said to be singular if it's determinant is zero.…

Q: The matrix 2 48 A= 0 2 -2 -1 28] has one real eigenvalue. Find this eigenvalue, its multiplicity,…

A:

Q: , a linear operator and a scalar λ are given. Show that is an eigenvalue of the operator and…

A:

Q: Find cond1(A ) and cond∞(A). State whether th e given matrix is ill-conditioned.

A: To find:  and

Q: 6 -4 For the matrix A find a matrix C such that C-1AC is in canonical form and 1 state the canonical…

A: Given matrix is A=6−412. We have to find he matrix C such that C−1AC is in canonical form and state…

Q: 3 1.2 Given X = =[-³₁₁³] and Y = [-23 19]. 0 show that (X-Y)(X+Y) # x² - y²

A:

Q: 8. Suppose 2 is an eigenvalue of an invertible matrix A. Prove that is an eigenvalue of kA-¹ for…

A:

Q: Prove that if A is an eigenvalue of the n x n matrix A, then is also an eigenvalue of AT.

A:

Q: Let 4 = ²₁ 4 =1²2₂2₂] 2. a. Give the characteristic equation of A and verify that A satisfies the…

A:

Q: 4 8. 5. Let C = 0. the cofactor matrix of a matrix A and let 7. -7 9] 611 b12 b13 A the inverse…

A:

Q: 1. If 1+ A is nonsingular, show that (I+ A)"' and I– A commute and (I + A) +(I+ A')"=1, where I is…

A: Given I+A is nonsingular and we have to show that I+A-1 and I-A commute and  I+A-1+I+A-1-1=I

Q: 4. Let A be an nxn real matrix such that A is diagonalizable and A has only a single eigenvalue A…

A: