lgemectirs (1 point) lf v,-| | | are eigenvectors of a matrix A corresponding to the...
Let A be a 2x2 matrix with eigenvalues 4 and and corresponding eigenvectors V, = and v2 Let} be a solution of the difference equation X: 1 -AX. Xo' - a Computex, = Ax (Hint: You do not need to know itselt b. Find a formula for x, involving k and the eigenvectors V, and v2 a x Ax=(Type an integer or simplified fraction for each matrix element) b. xxv.v2 (Type expressions using k as the variable.)
Please solve in details. Show that, u, v, w are orthonormal eigenvectors of matrix M, corresponding to eigenvalues 1, 12, 13 respectively, and L is a square matrix whose columns are u, v, w , then (D = Ll' (M L ) is a diagonal matrix.
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=
11. Find the eigenvalues and corresponding eigenvectors of the following matrix using Jacobi's method. [1 / 2 A= V2 3 2 1 2 2 1
Let A be a 2x2 matrix with eigenvalues 5 and 3 and corresponding eigenvectors V1 = | Let {XK) be a solution of the difference equation asmenn :)--[;)] wywood 11 **+1 = Axx, Xo = a. Computex, = Axo. (Hint: You do not need to know A itself.] b. Find a formula for xk involving k and the eigenvectors V, and V2.
and v2-0 | are eigenvectors or a matnx A corresponding to the eigenvalues λι-5 and λ2 -4, respectively. (1 point) if v, = then A(v, + v2)- and A(-2y)- Note: Input a vector using angle brackets and commas. For example, enter 2 as "<1,2,3>". For more information, click help (vectors).
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.
[10 pointsjConsider an orthogonal matrix Q, which has two nonzero orthogonal eigenvectors v1 and v2 whose corresponding eigenvalues are λι = 3 and λ2-4, respectively. Now consider a vector y = Vi + vȚvayı + λ2V2 and compute 1QTQQy in terms of the eigenvectors and eigenvalues of Q 4. [10 pointsjConsider an orthogonal matrix Q, which has two nonzero orthogonal eigenvectors v1 and v2 whose corresponding eigenvalues are λι = 3 and λ2-4, respectively. Now consider a vector y =...
Problem 2. Find the eigenvalues Xi and the corresponding eigenvectors v; of the matrix -4 6 -12 A-3 -16, (3 3 8 and also find an invertible matrix P and a diagonal matrix D such that D=P-AP or A = PDP-
Find the eigenvalues and corresponding eigenvectors for the matrix [1 -1 1] To 3 2 if the characteristic equation of the matrix is 2-107. +292 + 20 = 0.