Q7. (a) Find a basis for the eigenspace of the following matrix corresponding to the eigenvalue...
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?
12.3. Eigenspace basis 0.0/10.0 points (graded) The matrix A given below has an eigenvalue = -16. Find a basis of the eigenspace corresponding to this eigenvalue. [-8 0 -81 A= 4 -16 -4 | 4 0 -20] How to enter a set of vectors. In order to enter a set of vectors (e.g. a spanning set or a basis) enclose entries of each vector in square brackets and separate vectors by commas. For example, if you want to enter the...
This Question: 1pl 1 of 30 (0 complete) Find a basis for the eigenspace corresponding to the eigenvalue. - 1 A= 81 - 6 1 22 6 2=7 5 A basis for the eigenspace corresponding to a = 7 is {} (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Us Enter your answer in the answer box hp
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....
is an eigenvalue invertible matrix with X as an eigenvalue. Show that of A-1. Suppose v ER is a nonzero column vector. Let A (a) Show that v is an eigenvector of A correspond zero column vector. Let A be the n xn matrix vvT. n eigenvector of A corresponding to eigenvalue = |v||2. lat O is an eigenvalue of multiplicity n - 1. (Hint: What is rank A?) (b) Show that 0 is an eigenvalue of
Suppose that λ = 1 is an eigenvalue for matrix A. Find a basis for the eigenspace corresponding to this eigenvalue. A = 3 6 −2 0 1 0 0 0 1
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
This Question: 4 pts 3 of 30 (0 complete) Find a basis for the eigenspace corresponding to the elgenvalue. A= 6 -3 -2 8 2.2 = 5 6 9 A basis for the eigenspace corresponding to 2 = 5 is } (Type a vector or list of vectors. Type an integer or simplified fraction for each matrix element. Use a comma to separate answers as needed)
4 2 3 13. Find a basis for the eigenspace of the matrix A1 1- corresponding to the 2 49 eigenvalue -3. [4 points.]
Let the matrix below act on C? Find the eigenvalues and a basis for each eigenspace in c? 1 2 - 2 1 1 2 The eigenvalues of - 2 1 (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.) are A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is (Type an exact answer, using radicals and i as needed.) A basis for the eigenspace...