12. (1(a) You are given an n x n real anti-symmetric matrix A (i.e. A" = -A) and x € R".(i) ( s) What is the size of x" Ax?s) Prove that x" Ax = 0.- ) Determine whether there exists a 3 x 3 real symmetric matrix whose eigenvalues are(ii)(b) (гA1 = -1, Ag = 3, Az = 7and for which the corresponding eigenvectors are as follows:Vi =Va =V3If there is such a matrix, find it, and if there is none, explain why not.

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12. (1 (a) You are given an n x n real anti-symmetric matrix A (i.e. A" = -A) and x € R". %3D +s) What is the size of x" Ax? s) Prove that x" Ax = 0. - ) Determine whether there exists a 3 x 3 real symmetric matrix whose eigenvalues are (i) ( (ii) (b) ( d1 = -1, A2 = 3, A3 = 7 and for which the corresponding eigenvectors are as follows: V2 = V3 If there is such a matrix, find it, and if there is none, explain why not.

12. (1 (a) You are given an n x n real anti-symmetric matrix A (i.e. A" = -A) and x € R". %3D +s) What is the size of x" Ax? s) Prove that x" Ax = 0. - ) Determine whether there exists a 3 x 3 real symmetric matrix whose eigenvalues are (i) ( (ii) (b) ( d1 = -1, A2 = 3, A3 = 7 and for which the corresponding eigenvectors are as follows: V2 = V3 If there is such a matrix, find it, and if there is none, explain why not.

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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