2. Find eigenvalues and eigenvectors of the matrix and check if they are linearly independent A...
3. ( Find all eigenvalues and eigenvectors of the matrix A= [ 5 | 3 -1] and show the eigen- 1 vectors are linearly independent.
Find two linearly independent set of eigenvectors for the matrix and then solve 1 2 2. -2 6
Find the matrix A that has the given eigenvalues and corresponding eigenvectors. Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A= Find the matrix A that has the given eigenvalues and corresponding eigenvectors. 2 A=
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) }
1. Is it possible to find three linearly independent eigenvectors for A? 0 0 0 (1) A= 0 0 0 The eigenvalues of A are 11 = 12 = 0; 13 = 1 0 0 1 1 6 0 (2) A= 0 2 1 The eigenvalues of A are 11 = 3; 12 = 13 = 1 0 1 2 9 40 (3) A -6 -1 0 The eigenvalues of A are 11 = 12 = 3; 13 = 5...
Find the eigenvalues and associated eigenvectors of the matrix Q2: Find the eigenvalues and associated eigenvectors of the matrix 7 0 - 3 A = - 9 2 3 18 0 - 8
3. Find all the eigenvalues and corresponding eigenspaces for the matrix B = 4. Show that the matrix B = 0 1 is not diagonalizable. 0 4] Lo 5. Let 2, and 1, be two distinct eigenvalues of a matrix A (2, # 12). Assume V1, V2 are eigenvectors of A corresponding to 11 and 22 respectively. Prove that V1, V2 are linearly independent.
(1 point) Consider the linear system a. Find the eigenvalues and eigenvectors for the coefficient matrix. , and 12 = -:| b. For each eigenpair in the previous part, form a solution of ý' = Ay. Use t as the independent variable in your answers. ý (t) = and yz(t) = c. Does the set of solutions you found form a fundamental set (i.e., linearly independent set) of solutions? Choose
12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/4 0 -1; 01/26; 1/204) (20 pts)Find the inverse of the matrix from question 12. I te To keep up-to-date with security updates, fixes, and improvements, choose Check for Upd c (2-1) 12) (20 pts total) Find the eigenvalues and eigenvectors of the following matrix, Choose x1=1: [2/40-1; 01/26;1/204) (20 pts) Find the inverse of the matrix from question 12.
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.