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Question 7. The linear operator L on R3 with the Euclidean inner product is defined by 1 1 1 L(X) = AX, where A = 1 1 %3D -1 1 1 -1 1) Is L orthogonally diagonalizable? Justify your answer. 2) If L is orthogonally diagonalizable, find an orthonormal basis where the matrix of

Question 7. The linear operator L on R3 with the Euclidean inner product is defined by 1 1 1 L(X) = AX, where A = 1 1 %3D -1 1 1 -1 1) Is L orthogonally diagonalizable? Justify your answer. 2) If L is orthogonally diagonalizable, find an orthonormal basis where the matrix of

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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8. Can someone please help me with this? How do you solve this and justify it? - taken from my practice questions from textbook algebra 101 @ NYU

Question 7. The linear operator L on R with the Euclidean inner product is defined by: 1 1 1 L(X)= AX, where A = 1 -1 1 1 1 -1 1) Is L orthogonally diagonalizable? Justify your answer. 2) If L is orthogonally diagonalizable, find an orthonormal basis where the matrix of L is diagonal, the corresponding diagonal matrix and transition matrix.
Transcribed Image Text:Question 7. The linear operator L on R with the Euclidean inner product is defined by: 1 1 1 L(X)= AX, where A = 1 -1 1 1 1 -1 1) Is L orthogonally diagonalizable? Justify your answer. 2) If L is orthogonally diagonalizable, find an orthonormal basis where the matrix of L is diagonal, the corresponding diagonal matrix and transition matrix.
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