Suppose that n = 2 3. -Let A: RR" be an operator that leaves a subspace ECR invariant.Let x: R→→ Rn be a solution of x' Ax. If x (to) E E for some to ER, showthat x(t) € E for all t € R.

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Answered: 3. Let A: RnR be an operator that…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter5: Inner Product Spaces

Section5.CR: Review Exercises

Problem 47CR: Find an orthonormal basis for the subspace of Euclidean 3 space below. W={(x1,x2,x3):x1+x2+x3=0}

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3. Let A: RnR be an operator that leaves a subspace E C Rª invariant. Let x: RR” be a solution of x' Ax. If x (to) € E for some to € R, show that x(t) € E for all t € R. -