Question

In: Advanced Math

Find the matrix P that diagonalizes A, and check your work by computer P^-1AP. This matrix...

Find the matrix P that diagonalizes A, and check your work by computer P^-1AP. This matrix is

[-14 12]

[-20 17]

I've tried this problem, and I keep getting the eigenvalues of λ=1, 2 and the eigenspace [4 5] for λ=1, and eigenspace [3 4] for λ=2. However, whenever I check it with P^-1AP, it doesn't produce a diagonal matrix.

Solutions

Expert Solution


Related Solutions

For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal....
For the matrix A, find (if possible) a nonsingular matrix P such that P−1AP is diagonal. (If not possible, enter IMPOSSIBLE.) A = 2 −2 3 0 3 −2 0 −1 2 P = Verify that P−1AP is a diagonal matrix with the eigenvalues on the main diagonal. P−1AP =
Diagonalize the matrix (That is, find a diagonal matrix D and an invertible matrix P such...
Diagonalize the matrix (That is, find a diagonal matrix D and an invertible matrix P such that A=PDP−1. (Do not find the inverse of P). Describe all eigenspaces of A and state the geometric and algebraic multiplicity of each eigenvalue. A= -1 3 0 -4 6 0 0 0 1
(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal...
(2) A matrix A is given. Find, if possible, an invertible matrix P and a diagonal matrix D such that P −1AP = D. Otherwise, explain why A is not diagonalizable. (a) A =   −3 0 −5                 0 2 0                 2 0 3 (b) A =   2 0 −1              1 3 −1              2 0 5 (c) A = 1 −1 2              −1 1 2               2 2 2
Find an orthogonal matrix P that diagonalizes the following matrix A: A is 3 by 3...
Find an orthogonal matrix P that diagonalizes the following matrix A: A is 3 by 3 matrix: (3 1 0 1 -1 1 0 0 2)
Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0...
Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0 3 0 / 0 0 3 ] and compute P ?1AP.
Find the matrix A representing the follow transformations T. In each case, check that Av =...
Find the matrix A representing the follow transformations T. In each case, check that Av = T(v) T(T(x,y,z)) where T(x,y,z)=(x-3y+4z, 6x-2z, 8x-y-4z)
Find the matrix A representing the follow transformations T. In each case, check that Av =...
Find the matrix A representing the follow transformations T. In each case, check that Av = T(v) Step by step please. A. T(x,y,z) = (x-3y+4z, 6x-2z, 8x-y-4z) B. T(x,y) = (x,y,y-x,x+y, 6x-9y) Thank you!
- for the transition matrix P= 0.8 0.2 0.0 , solve the equation SP=S to find...
- for the transition matrix P= 0.8 0.2 0.0 , solve the equation SP=S to find the stationary matrix S and the limiting matrix P. 0.5 0.1 0.4 0.0 0.6 0.4
Find the adjoint of matrix A, the determinant of matrix A, and the determinant of the...
Find the adjoint of matrix A, the determinant of matrix A, and the determinant of the adjoint A. A= 1 1 0 2 2 1 1 0 0 2 1 1 1 0 2 1
Let A be an m × n matrix and B be an m × p matrix....
Let A be an m × n matrix and B be an m × p matrix. Let C =[A | B] be an m×(n + p) matrix. (a) Show that R(C) = R(A) + R(B), where R(·) denotes the range of a matrix. (b) Show that rank(C) = rank(A) + rank(B)−dim(R(A)∩R(B)).
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT