Question

Find the real symmetric 3 x 3 matrix with eigenvalues $\lambda_1 = -1, \lambda_2 = -4, \lambda_3 = -4$ and corresponding mutually orthogonal eigenvectors $v_1 = \begin{bmatrix} 4 \\ 5 \\ -1 \end{bmatrix}$, $v_2 = \begin{bmatrix} 3 \\ -3 \\ -3 \end{bmatrix}$, $v_3 = \begin{bmatrix} -2 \\ 1 \\ -3 \end{bmatrix}$ Check

Name: find the real symmetric 3 x 3 matrix with eigenvalues lambda1 1 lambda2 4 lambda3 4 and corresponding mutually orthogonal eigenvectors v1 beginbmatrix 4 5 1 endbmatrix v2 beginbmatrix 3 80693
Uploaded: 2023-04-06T13:47:44-08:00
Duration: 5 min 5 s
Channel: Supreeta N
Description: find the real symmetric 3 x 3 matrix with eigenvalues lambda1 1 lambda2 4 lambda3 4 and corresponding mutually orthogonal eigenvectors v1 beginbmatrix 4 5 1 endbmatrix v2 beginbmatrix 3 80693

          Find the real symmetric 3 x 3 matrix with eigenvalues $\lambda_1 = -1, \lambda_2 = -4, \lambda_3 = -4$ and corresponding mutually orthogonal eigenvectors

$v_1 = \begin{bmatrix} 4 \\ 5 \\ -1 \end{bmatrix}$, $v_2 = \begin{bmatrix} 3 \\ -3 \\ -3 \end{bmatrix}$, $v_3 = \begin{bmatrix} -2 \\ 1 \\ -3 \end{bmatrix}$

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find the real symmetric 3 x 3 matrix with eigenvalues lambda1 1 lambda2 4 lambda3 4 and corresponding mutually orthogonal eigenvectors v1 beginbmatrix 4 5 1 endbmatrix v2 beginbmatrix 3 80693

Added by Angela W.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

04/06/2023

Step 1

$||v_1|| = \sqrt{4^2 + 5^2 + (-1)^2} = \sqrt{16 + 25 + 1} = \sqrt{42}$ $||v_2|| = \sqrt{3^2 + (-3)^2 + (-3)^2} = \sqrt{9 + 9 + 9} = \sqrt{27} = 3\sqrt{3}$ $||v_3|| = \sqrt{(-2)^2 + 1^2 + (-3)^2} = \sqrt{4 + 1 + 9} = \sqrt{14}$ $u_1 = \frac{v_1}{||v_1||} = Show more…

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Find the real symmetric 3 x 3 matrix with eigenvalues $\lambda_1 = -1, \lambda_2 = -4, \lambda_3 = -4$ and corresponding mutually orthogonal eigenvectors $v_1 = \begin{bmatrix} 4 \\ 5 \\ -1 \end{bmatrix}$, $v_2 = \begin{bmatrix} 3 \\ -3 \\ -3 \end{bmatrix}$, $v_3 = \begin{bmatrix} -2 \\ 1 \\ -3 \end{bmatrix}$ Check