Let A = 2 −5 7 4 . The vector −1 − √ 34i 7 is an eigenvector for A with eigenvalue 3 − √ 34i. Find the other eigenvalue and a vector in its eigenspace Answers: a) 3 + √ 34i, −1 − √ 34i 7 b) 3 − √ 34i, 1 + √ 34i 7 c) 3 + √ 34i, −1 + √ 34i 7
see photo
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Let A = 2 −5 7 4 . The vector −1 − √ 34i 7 is an eigenvector for A with eigenvalue 3 − √ 34i. Find the other eigenvalue and a vector in its eigenspace Answers: a) 3 + √ 34i, −1 − √ 34i 7 b) 3 − √ 34i, 1 + √ 34i 7 c) 3 + √ 34i, −1 + √ 34i 7 see
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -1 6 2 16 2 -1 8 (b) Suppose that the vector z is an eigenvector of the matrix A corresponding to the eigenvalue 4. Let n be a positive integer. What is A"r equal to?
Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue X= 2: 4 -16 2 1 6 2 -1 8 (b) Suppose that the vector r is an eigenvector of the matrix A corresponding to the eigenvalue 1. Let n be a positive integer. What is A" equal to?
Find the eigenspace corresponding to each eigenvalue
of
a.
b.
c.
d.
e.
f.
Find the eigenspace corresponding to each eigenvalue of A 3 8 (5) = 8A(-2) = 4 b. A- [12] {{ }) {{}) 841-2) = {{{ z?}) 841) = {{ --]) {[ -> ]}) 843) = {{{ 2 }) ( =>]}) 842) = 812) = {{{1}) 8A(7) = d. 8A(-5) = e. 8A(-1) = 8A(-3) = f. 8A(-1) = {}}}) 844) = {{{ ["}}
Let A be a square matrix with eigenvalue λ and
corresponding eigenvector x.
Annment 5 Caure MATH 1 x CGet Homewarcx Enenvalue and CAcademic famxG lgeb rair mulbip Redured Rew F x Ga print sereenx CLat A BeA Su Agebrair and G Shep-hy-Step Ca x x x C https/www.webessignnet/MwebyStudent/Assignment-Responses/submit7dep-21389386 (b) Let A be a squara matrix with eigenvalue a and comasponding aigenvector x a. For any positive integer n, " is an eigenvalue of A" with corresponding eigenvector x b....
4. (a) (6 marks) Let A be a square matrix with eigenvector v, and corresponding eigenvalue 1. Let c be a scalar. Show that A-ch has eigenvector v, and corresponding eigenvalue X-c. (b) (8 marks) Let A = (33) i. Find the eigenvalues of A. ii. For one of the eigenvalues you have found, calculate the corresponding eigenvector. iii. Make use of part (a) to determine an eigenvalue and a corresponding eigenvector 2 2 of 5 - 1
5. Let A, B E Mmxm(R) and let v be an eigenvector of A with eigenvalue 1, and v be an eigenvector of B with eigenvalue j. (a) Show that v is an eigenvector of AB. What is the corresponding eigenvalue? (b) Show that v is an eigenvector of A+B. What is the corresponding eigenvalue?
Find the eigenspace corresponding to each eigenvalue of A A 1 3 4 2
(1 point) Find a basis of the eigenspace associated with the eigenvalue 3 of the matrix 1 0 -4 2 3 4 1 0 5 A= 3 3 C Abasis for this eigenspace is 0 -2 0 0 1
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A. What is its eigenvalue? (b) By solving (A+2/)x 0, show that -2 is an eigenvalue of A. (c) Use the results of parts (a) and (b) to write down all eigenvalues of A along with their algebraic and geometric multiplicities. Is A diagonalizable? (Note: This question does not require finding eigenvalues by solving det(A XI) 0)
5. Let -2 0 2AA8 (a) Show thatis an eigenvector of A....
3 7. If A is a 3x3 matrix with eigenvector o corresponding to an 1-21 eigenvalue of 5 and 2 corresponding to an eigenvalue of 2, and v= 7 [10] 4 find Av. 6