In each of Problems 17 through 20, use a computer to find the eigenvalues and eigenvectors for the given matrix.
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- Sölvé the following: 3 1 -6 a. Find the inverse matrix (A¯') if the matrix A = 2 -1 -4 3arrow_forwardFor each of the following, factor the matrix A into a product Q DQ" where Q is orthogonal and D is diagonal. -5 -1 -1 (a) A =-1 -3 -1 -1 -3 Q = D = %3Darrow_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
- In 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_forwardYou are provided with the following matrix B (where the 2nd and 3rd rows are not given), and vector x. Given that x is an eigenvector of the matrix A, what would be the corresponding eigenvalue? B = -10 -10 10 x= 2 * * * 4 * * * 4arrow_forwardLet A, B, and C be an n x n invertible matrices. Solve the following equation for X. Justify each step in your solution. A-1(A+ X)B = C.arrow_forward
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