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Question 10 [10 points] Find the basic eigenvectors of A corresponding to the eigenvalue . -3...
Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue 2 12 6 A 0 -14 -8 0 24 14 Number of distinct eigenvalues: 1 Number of Vectors: 1 030
Find the basic eigenvectors of A corresponding to the eigenvalue 2. (15 -6 -18 0] 15 -2 -15 0 A= 12 -6 -15 0 , a = -3 30 –6 –30 1 Number of Vectors: 1
Find all distinct eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. [o -6 -61 A = 0 -7 -6 10 4 3 Number of distinct eigenvalues: 1 Number of Vectors: 1 C
Find all distinct (real or complex) eigenvalues of A. Then find the basic eigenvectors of A corresponding to each eigenvalue. For each eigenvalue, specify the number of basic eigenvectors corresponding to that eigenvalue, then enter the eigenvalue followed by the basic eigenvectors corresponding to that eigenvalue. A= 17 18 |-13 -13 Number of distinct eigenvalues: 1 Number of Vectors: 1
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 ]
Find the eigenvalues and number of independent eigenvectors. (Hint: 4 is an eigenvalue.) 10 -6 12 -8 0 0 | 12 -7 -1 a) Eigenvalues: 4,4, -1; Number of independent eigenvectors: 2 b) Eigenvalues: 4,2, -1; Number of independent eigenvectors: 3 c) Eigenvalues: 4,-2,1; Number of independent eigenvectors: 3 d) Eigenvalues: 4,-2, -1; Number of independent eigenvectors: 3 e) Eigenvalues: 4,-2, -2; Number of independent eigenvectors: 2 f) None of the above.
Question 3 [8 points] Find all values of x so that the triangle with vertices A(-2, x, -1), B(-4, 2, -3), and C(-3, 1,-5) has area x=??? 3 Official Time: 22:11:23 SUBMIT AND MARK SAVE AND CLOSE
Corresponding eigenvectors of each eigenvalue 9 Let 2. (as find the eigenvalues of A GA 1 -- 1 and find the or A each 5 Find the corresponding eigenspace to each eigen value of A. Moreover, Find a basis for The Corresponding eigenspace (c) Determine whether A is diagonalizable. If it is, Find a diagonal matrix ) and an invertible matrix P such that p-AP=1
2 -25 4)[10+10+10pts.) a) Find the eigenvalues and the corresponding eigenvectors of the matrix A = b) Find the projection of the vector 7 = (1, 3, 5) on the vector i = (2,0,1). c) Determine whether the given set of vectors are linearly independent or linearly dependent in R" i) {(2,-1,5), (1,3,-4), (-3,-9,12) } ii) {(1,0,0,0), (0,1,0,0), (0,0,1,0), (0,0,0,1) }
Question 7 [10 points] For the matrix A below, find a value of k so that A has two basic eigenvectors associated with the eigenvalue 1 - -1. A = 293 6 0-1 4k 0 0 -3 -2 0 0 0 -1 k = 0