Find (as a unit vector with negative first term) an eigenvector of the matrix
corresponding to the eigenvalue lambda = 2
Find (as a unit vector with negative first term) an eigenvector of the matrix corresponding to...
two seperate questions multiple choice Determine if the vector is an eigenvector of a matrix. If it is, determine the corresponding eigenvalue. A= 1 1 1 and v The eigenvalue is 2. The eigenvalue is 0. The eigenvalue is 3. v is not an eigenvector. Find the inverse of the matrix, if it exists. A= -1-6 6 3 2 11 11 1 11 33 33 NE -= 2 11 = -18 = -1= 야야 O
The matrix A= is diagonalisable with eigenvalues 1, -2 and -2. An eigenvector corresponding to the eigenvalue 1 is . Find an invertible matrix M such that M−1AM= ⎛⎝⎜⎜⎜1000-2000-2⎞⎠⎟⎟⎟. Enter the Matrix M in the box below. Question 8: Score 0/2 1 3 -3 4 6 -6 8 The matrix A = 1-6 6 | is diagonalisable with eigenvalues 1,-2 and-2. An eigenvector corresponding to the eigenvalue 1 is -2 2 1 0 0 0 0-2 Find an invertible matrix...
For the given matrix and eigenvalue, find an eigenvector corresponding to the eigenvalue. -4 A = X = 5 48-11
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
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?
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
In Problems 1 through 23, find an eigenvector corresponding to each eigenvalue of the given matrix. 15. 3 0 -17 23 2 -1 ( 3 2 . 5 -7 17.4 -1 -3 2 0 2010 0 10 01 -10 24. Find unit eigenvectors (i.e., eigenvectors whose magnitudes equal unity) for the matrix in Problem 1. 1. [-1 ]
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find 1 and i. i = has an eigenvector ū =
Find all eigenvalues and eigenvector of the matrix 2 2 A 1 1 -2 -4-1 Give the eigenvalues in ascending order. Choose the corresponding eigenvectors from the table below: 0 1 -2 2 1 V 2 = A 0 2 Vector 1 Vector 2 Vector 3 Vector 4 Vector 5 Vector 6 Eigenvector number: Eigenvector number: A3 Eigenvector number: Il