True false only!Need 4-10 4) If the linear map T : C → C³ is diagonalizable and has 1,9 as its only eigenvalueseigenvalues, then its characteristic and minimal polynomials are the same.5) If SE L(V) is an isometry on the inner product space V, then S - I is alwaysinvertible.6) If N E L(V) is nilpotent then so is I + N².7) If the product AB of the matrices A € Matm,n(F) and B € Mat,m(F) is non-singular so is the product BA.8)(2 3 1= 12.0 2 3)det 0 0 39) Consider R? with its Euclidean inner product. There exists three non-zero vectorsin R², which are mutually orthogonal.10) If A € Mat,, is diagonalizable it admits n linearly independent eigenvectors.

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Answered: 4) If the linear map T : C → C is…

4) If the linear map T : C → C is diagonalizable and has 1,9 as its only eigenvalues eigenvalues, then its characteristic and minimal polynomials are the same.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.3: Orthonormal Bases:gram-schmidt Process

Problem 17E: Complete Example 2 by verifying that {1,x,x2,x3} is an orthonormal basis for P3 with the inner...

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Question

True false only! Need 4-10

4) If the linear map T : C → C³ is diagonalizable and has 1,9 as its only eigenvalues
eigenvalues, then its characteristic and minimal polynomials are the same.
5) If SE 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 € Matm,n(F) and B € Mat,m(F) is non-
singular so is the product BA.
8)
(2 3 1
= 12.
0 2 3)
det 0 0 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,, is diagonalizable it admits n linearly independent eigenvectors.

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