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)

Expert Solution

Colby Messinger answered 2 years ago

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 =

(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4...

(a) Find the matrix representation for the orthogonal projection Pr : R 4 → R 4 onto the plane P= span 1 -1 -1 1 -1 -1 1 1 (b) Find the distance of vector ~y = 2 0 0 4 from the plane P.

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

Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such...

Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal matrix D such that QTAQ = D. (Enter each matrix in the form [[row 1], [row 2], ...], where each row is a comma-separated list.) A = 5 0 0 0 1 3 0 3 1 (D, Q) = $$ Incorrect: Your answer is incorrect. Submission 2(0/1 points)Monday, November 25, 2019 10:01 PM CST Orthogonally diagonalize the matrix by finding an orthogonal matrix Q and a diagonal...

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.

(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 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 a nonzero vector orthogonal to the plane through the points P, Q, and R

Consider the points below. P(0, -3,0), Q(5,1,-2), R(5, 2, 1) (a) Find a nonzero vector orthogonal to the plane through the points P, Q, and R. (b) Find the area of the triangle PQR. (Recall the area of a triangle is one-half the area of the parallelogram.)

Find the family of curves orthogonal to: y4 = k(x − 2)3.

(a) Find a 3×3 matrix A such that 0 is the only eigenvalue of A, and...

(a) Find a 3×3 matrix A such that 0 is the only eigenvalue of A, and the space of eigenvectors of 0 has dimension 1. (Hint: upper triangular matrices are your friend!) (b) Find the general solution to x' = Ax. PLEASE SHOW YOUR WORK CLEARLY.

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