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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.

Expert Solution

Solution: The characteristic equation is

for

By and

Put

for

Put and

is an eigenvector corresponding to

Since Algebraic multiplicity of Geometric multiplicity of and

Algebraic multiplicity of Geometric multiplicity of

is diagonalisable

milcah answered 2 years ago

(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

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 =

find all eigenvalues and eigenvectors of the given matrix A= [1 0 0 2 1 -2...

find all eigenvalues and eigenvectors of the given matrix A= [1 0 0 2 1 -2 3 2 1]

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

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.

Find the inverse of the matrix A= 2 -1 3 0 1 1 -1 -1 0

Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1...

Given a matrix A = [?1 ? ? 0 ?2 ? 0 0 ?2], with ?1 ≠ ?2 and ?1, ?2 ≠ 0, A) Find necessary and sufficient conditions on a, b, and c such that A is diagonalizable. B) Find a matrix, C, such that C-1 A C = D, where D is diagonal. C) Demonstrate this with ?1 = 2, ?2 = 5, and a, b, and c chosen by you, satisfying your criteria from A).

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Find a matrix P that diagonalizes the matrix A = [ 2 0 ?2 / 0...

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