Question

(2) Orthogonally diagonalize the following matrix by finding the diagonal matrix D and orthogonal matrix P such that $A = PDP^T$. $$A = \begin{bmatrix} 2 & 2 & 1 \\ 2 & -1 & -2 \\ 1 & -2 & 2 \end{bmatrix}$$ (Hint: The eigenvalues are $\lambda = 3, 3, -3$.)

Name: 2 orthogonally diagonalize the following matrix by finding the diagonal matrix d and orthogonal matrix p such that a pdpt a beginbmatrix 2 2 1 2 1 2 1 2 2 endbmatrix hint the eigenvalues are 33832
Uploaded: 2021-12-30T08:30:48-08:00
Duration: 1 min 8 s
Channel: Hast Aggarwal
Description: 2 orthogonally diagonalize the following matrix by finding the diagonal matrix d and orthogonal matrix p such that a pdpt a beginbmatrix 2 2 1 2 1 2 1 2 2 endbmatrix hint the eigenvalues are 33832

          (2) Orthogonally diagonalize the following matrix by finding the diagonal matrix D and orthogonal matrix P such that $A = PDP^T$.
$$A = \begin{bmatrix} 2 & 2 & 1 \\ 2 & -1 & -2 \\ 1 & -2 & 2 \end{bmatrix}$$
(Hint: The eigenvalues are $\lambda = 3, 3, -3$.)

2 orthogonally diagonalize the following matrix by finding the diagonal matrix d and orthogonal matrix p such that a pdpt a beginbmatrix 2 2 1 2 1 2 1 2 2 endbmatrix hint the eigenvalues are 33832

Added by Melody P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Hast Aggarwal

12/30/2021

Step 1

For $\lambda = 3$, we solve $(A - 3I)v = 0$: $$A - 3I = \begin{bmatrix} 2-3 & 2 & 1 \\ 2 & -1-3 & -2 \\ 1 & -2 & 2-3 \end{bmatrix} = \begin{bmatrix} -1 & 2 & 1 \\ 2 & -4 & -2 \\ 1 & -2 & -1 \end{bmatrix}$$ The rows are linearly dependent, so we have $-x + 2y + z Show more…

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(2) Orthogonally diagonalize the following matrix by finding the diagonal matrix D and orthogonal matrix P such that $A = PDP^T$. $$A = \begin{bmatrix} 2 & 2 & 1 \\ 2 & -1 & -2 \\ 1 & -2 & 2 \end{bmatrix}$$ (Hint: The eigenvalues are $\lambda = 3, 3, -3$.)