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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
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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No explanation need just T/F for 5,6,7,8,9,10
5) If S E L(V) is an isometry on the inner product space V, then S – I is always invertible. 6) If N E L(V) is nilpotent then so is I+ N². 7) If the product AB of the matrices A € Mat,m,n(F) and B e 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 R², which are mutually orthogonal. 10) If A € Mat,,n is diagonalizable it admits n linearly independent eigenvectors.
Transcribed Image Text:5) If S E L(V) is an isometry on the inner product space V, then S – I is always invertible. 6) If N E L(V) is nilpotent then so is I+ N². 7) If the product AB of the matrices A € Mat,m,n(F) and B e 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 R², which are mutually orthogonal. 10) If A € Mat,,n is diagonalizable it admits n linearly independent eigenvectors.
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