In each of Problems 1 through 10, find all eigenvalues and eigenvectors of the given matrix.
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- FIND the eigenvalues of the following matrix: [−3 −1] B= [ 2 −5]arrow_forwardPlease solve this question in handwriting. step by step. I am confused. Again please solve in handwritting.arrow_forwardIn this problem, if you give decimal answers then give at least three digits of accuracy beyond the decimal. The matrix has the following complex eigenvalues (give your answer as a comma separated list of complex numbers; use "i" for ✓-1 and feel free to use a computer to solve the relevant quadratic equation): λ = 1.65+1.548386257i, 1.65-1.548386257i Since A has non-real eigenvalues, it is not diagonalizable, but we can find a matrix C = section 5.5 of Lay): C = P = cos(6) A = sin(8) -sin(8) cos(8) [113] 1.8 Further, we may factor Cas C = XY, where X is a matrix that scales by the positive real number radians, with —π/2 ≤0 ≤ π/2) is and an invertible matrix P such that A = PCP-¹ (I want you to cook up C, P as in and Y is rotation matrix whose counter-clockwise rotation angle (in This means that if we let B be the basis for R² consisting of the columns of P, then the B-matrix of A is C. So if we're willing to change our basis for IR², then the linear transformation x Ax really is just…arrow_forward
- Problem 7 Determine the eigenvalues and eigenspaces of the matrix A := 120 0 1 0 -1 2-2arrow_forwardAll parts pleasearrow_forwardAnswer the following. Show the solution. 2 -2 -4 A = |-2 1 4 51 1. Eigenvalues of matrix A. 2. Determinant of matrix A. 3. Inverse of matrix A. 4. Transpose of matrix Aarrow_forward
- Please show step-by-step solution and do not skip steps. Explain your entire process in great detail. Explain how you reached the answer you did.arrow_forwardShow every step for each problem. That is the only way I will understand how you solved the problem. Directions: For each part of the question, find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.arrow_forwardProblem Eight Diagonalize this matrix, whose eigenvalues are 2 and 8. Note: You only need to find P and D. Adjust the eigenvectors (by scaling) so that they have a 1 in the lowest nonzero position. [4 2 21 A = 2 4 2 2 2 4 Solution:arrow_forward
- Solve the following matrix system by using variation of parameters: - () () dx 5 1 x + 5e-t dt 4 -5e-t Note that the eigenvalues of the matrix are -1, –6 with respective eigenvectors () | 4.arrow_forwarddo a b c onlyarrow_forward-3 For problems 11, 12, and 13. Suppose A = 11) Find Col(A) 12) Find Null(A) 13) Is it possible to find Eigenvalues for matrix A?arrow_forward
- Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning