2 points) For which value of k does the matrix have one real eigenvalue of multiplicity...
(1 pt) For which value of l does the matrix have one real eigenvalue of multiplicity 2?
(8 points) [102] The matrix A= 0 3 0 (205 has a single real eigenvalue = 3 with algebraic multiplicity three (a) Find a basis for the associated eigenspace. Basis = { (b) is the matrix A defective? A. A is not defective because the eigenvectors are linearly independent O B. A is defective because the geometric multiplicity of the eigenvalue is less than the algebraic multiplicity c. A is defective because it has only one eigenvalue D. A is...
2) Let A be an nxn matrix with eigenvalue a of multiplicity n. Show that A is diagonalizable if and only if A= 21.
For the given Matrix B, find: 1. The algebraic multiplicity of each eigenvalue. 2. The geometric multiplicity of each eigenvalue. 3. The matrix B is it Diagonalizable? If YES, provide the matrices P and D. ( 22-1 B = 1 3 -1 (-1 -2 2
question about linear algebra
1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as an eigenvalue with algebraic multiplicity 1. The eigenvalue -2 has an associated eigenvector The eigenvalue 4 has an associated eigenvector
1 point) The matrix 16 0 -18 A 6 2 6 12 0-14 has λ =-2 as an eigenvalue with algebraic multiplicity 2, and λ = 4 as...
2) Let A be an nxn matrix with eigenvalue of multiplicity n. Show that Ais diagonalizable if and only if A = al.
Q1 Existence 5 Points Every square matrix has at least one eigenvalue. O True O False Save Answer Q2 Basis 5 Points Let A be an (n xn) matrix, and assume that A has n different eigenvalues, then there is a basis of R" consisting eigenvectors of A. O False O True Q3 Computation 5 Points [ 1 Find the algebraic and geometric multiplicity of the unique eigenvalue of 1 1 Write your answer in the form [a, g] where...
(1 point) The matrix. has an eigenvalue 1 of multiplicity 2 with corresponding eigenvector ü. Find 1 and i. i = has an eigenvector ū =
(2 points) The matrix To A = 5 1-5 0 -5 5 0] 0 0] has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. The eigenvalue 11 is and a basis for its associated eigenspace is The eigenvalue 12 is and a basis for its associated eigenspace is
92 (a) The matrix A= 2 -5 -4 has an eigenvalue 2 -4 -5 Two of the entries of A are replaced by I, y so that it will not be convenient to find the eigenvalues by an application. 5 An eigenvector of A corresponding to the eigenvalue is 1 Find the value of and enter your answer in the box below. X= Number (b) Suppose that characteristic equation of a 8 x 8 matrix M is (1 - 2)4...