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Give an example of a 3 × 3 matrix, B, such that all the following conditions hold: • B is not diagonal, • det(B) is equal to the last 3 digits of your student number, ● X. (Bx) < 0 for some x € R³.

Give an example of a 3 × 3 matrix, B, such that all the following conditions hold: • B is not diagonal, • det(B) is equal to the last 3 digits of your student number, ● X. (Bx) < 0 for some x € R³.

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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Let A be a n x n matrix with distinct and positive eigenvalues. For each i, 1 ≤ i ≤n, let v, be an eigenvector of A with eigenvalue X, such that the v; are mutually orthogonal unit vectors. That is, Vi. Vj = { 1. 9 0, for i= j, for i j.
Transcribed Image Text:Let A be a n x n matrix with distinct and positive eigenvalues. For each i, 1 ≤ i ≤n, let v, be an eigenvector of A with eigenvalue X, such that the v; are mutually orthogonal unit vectors. That is, Vi. Vj = { 1. 9 0, for i= j, for i j.
Give an example of a 3 x 3 matrix, B, such that all the following conditions hold: B is not diagonal, • det (B) is equal to the last 3 digits of your student number, ● x· (Bx) < 0 for some x € R³.
Transcribed Image Text:Give an example of a 3 x 3 matrix, B, such that all the following conditions hold: B is not diagonal, • det (B) is equal to the last 3 digits of your student number, ● x· (Bx) < 0 for some x € R³.
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