(1 point) Find the characteristic polynomial of the matrix 5 -5 A = 0 [ 5 -5 -2 5 0] 4. 0] p(x) = (1 point) Find the eigenvalues of the matrix [ 23 C = -9 1-9 -18 14 9 72 7 -36 : -31] The eigenvalues are (Enter your answers as a comma separated list. The list you enter should have repeated items if there are eigenvalues with multiplicity greater than one.) (1 point) Given that vi =...
(1 point) Find the determinant of the matrix [1 0 0 -2] M-1 0 3 0 To 3 0 Lo 1 -3 2 o det(M) =
(1 point) Find the eigenvalues of the matrix A . -19 6 0 0 -36 11 0 0 A= The eigenvalues are λ| < λ2 < λ3 < λ4, where has an eigenvector 12 has an eigenvector has an eigenvector 4 has an eigenvector Note: you may want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues
(1 point) Find the characteristic polynomial of the matrix -2-20 1 -1 0 p(x)
-10 0] (1 point) Find a non-zero 2 x 2 matrix A such that A2
(1 point) Find all possible values of a, if any, for which the matrix 6-2 0 A-1-2-6 0 is not diagonalizable. If there are no such values, write none.
A) B) (1 point) The matrix A= 1-3 0 [1 0 -4 0 -1] 0 -5 has one real eigenvalue. Find this eigenvalue and a basis of the eigenspace. The eigenvalue is -4 A basis for the eigenspace is (1 point) Find the solution to the linear system of differential equations x' y' = = 25x + 727 9 -9.2 – 26y satisfying the initial conditions x(0) = -18 and y(0) = 7. x(t) = y(t) =
Find the power of A for the matrix A = -1 0 0 0 - 1 0 0 0 0 OOOO OOOO 0 0 0 0 0 0 0 0 1 If A is the 2 x 2 matrix given by [aь A = cd and if ad - bc + 0, the inverse is given by d-b ad - bc Use the formula above to find the inverse of the 2 x 2 matrix (if it exists). (If an...
(1 point) Find the three distinct real eigenvalues of the upper-triangular matrix B= 5-7 0 0 7 -1 0 -97 -4 . 4 The eigenvalues are [Note: If there is more than one answer, separate them by commas. E.g. 1,2]
(1 point) Diagonalize the matrix 8 8 5 A= 7 7 -7 0 0 3 Namely, find an invertible matrix P and a diagonal matrix D such that P-1AP = D. P= O 0 D = 0 0 0 0