VI. TRUE or FALSE. Justify your answers concisely.1. If A € M₂ (C) then A* - A is Hermitian.2. Every eigenvector v of A € M₂ (R) is also an eigenvector of A².3. If A € M₂ (C) is skew-Hermitian then kA is also skew-Hermitian for k € C.

As per the question we are given the following statements and we have to justify whether they are…

TRUE or FALSE. Justify your answe swers concisely. 1. If A € M₂, (C) then A* - A is Hermitian. 2. Every eigenvector v of A € M₁ (R) is also an eigenvector of A². 3. If A € M₂ (C) is skew-Hermitian then kA is also skew-Hermitian for k € C.

TRUE or FALSE. Justify your answe swers concisely. 1. If A € M₂, (C) then A* - A is Hermitian. 2. Every eigenvector v of A € M₁ (R) is also an eigenvector of A². 3. If A € M₂ (C) is skew-Hermitian then kA is also skew-Hermitian for k € C.

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter7: Eigenvalues And Eigenvectors

Section7.1: Eigenvalues And Eigenvectors

Problem 76E: Define T:P2P2 by T(a0+a1x+a2x2)=(2a0+a1a2)+(a1+2a2)xa2x2. Find the eigenvalues and the eigenvectors...

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Question

VI. TRUE or FALSE. Justify your answers concisely.
1. If A € M₂ (C) then A* - A is Hermitian.
2. Every eigenvector v of A € M₂ (R) is also an eigenvector of A².
3. If A € M₂ (C) is skew-Hermitian then kA is also skew-Hermitian for k € C.

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