Question

For the matrix A, find (if possible) a nonsingular matrix P such that P?¹AP is diagonal. (If not possible, enter IMPOSSIBLE.) A = [ 8 -4 ] [ -2 1 ] P = [ 1 -4 ] [ ] Verify that P?¹AP is a diagonal matrix with the eigenvalues on the main diagonal. P?¹AP = [ ] [ ]

          For the matrix A, find (if possible) a nonsingular matrix P such that P?¹AP is diagonal. (If not possible, enter IMPOSSIBLE.)

A = [ 8 -4 ]
    [ -2 1 ]

P = [ 1 -4 ]
    [      ]

Verify that P?¹AP is a diagonal matrix with the eigenvalues on the main diagonal.

P?¹AP = [      ]
        [      ]

For the matrix A, find (if possible) a nonsingular matrix P such that P?¹AP is diagonal. (If not possible, enter IMPOSSIBLE.)

A = [ 8 -4 ]
[ -2 1 ]

P = [ 1 -4 ]
[ ]

Verify that P?¹AP is a diagonal matrix with the eigenvalues on the main diagonal.

P?¹AP = [ ]
[ ]

Added by Ryan B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sri K

09/01/2023

Step 1

Given matrix A: \[ A = \begin{bmatrix} -2 & -4 \\ -2 & 1 \end{bmatrix} \] \[ det(A - λI) = det\left(\begin{bmatrix} -2 & -4 \\ -2 & 1 \end{bmatrix} - \begin{bmatrix} λ & 0 \\ 0 & λ \end{bmatrix}\right) \] \[ = det\left(\begin{bmatrix} -2-λ & -4 \\ -2 & 1-λ Show more…

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For the matrix A, find (if possible) a nonsingular matrix P such that P^(-1)AP is diagonal. (If not possible, enter IMPOSSIBLE.) Verify that P^(-1)AP is a diagonal matrix with the eigenvalues on the main diagonal.