5) If SE L(V) is an isometry on the inner product space V, then S- I is always invertible. 6) If N € L(V) is nilpotent then so is I + N². 7) If the product AB of the matrices A € Mat,m,(F) and B € Mat,m(F) is non- singular so is the product BA. (2 3 1 det 0 0 3 = 12. (0 2 3) 9) Consider R? with its Euclidean inner product. There exists three non-zero vectors in R?, which are mutually orthogonal. 10) If A € Mat, is diagonalizable it admits n linearly independent eigenvectors.

5) If SE L(V) is an isometry on the inner product space V, then S- I is always invertible. 6) If N € L(V) is nilpotent then so is I + N². 7) If the product AB of the matrices A € Mat,m,(F) and B € Mat,m(F) is non- singular so is the product BA. (2 3 1 det 0 0 3 = 12. (0 2 3) 9) Consider R? with its Euclidean inner product. There exists three non-zero vectors in R?, which are mutually orthogonal. 10) If A € Mat, is diagonalizable it admits n linearly independent eigenvectors.

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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