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Chapter 7: Q3E (page 323)

Is v鈬赌an eigenvector ofA+2In? If so, what is the eigenvalue?

Short Answer

Expert verified

Yes. The required given value is位+2 .

Step by step solution

01

Define the eigenvector

Eigenvector: An eigenvector of A is a nonzero vector V in Rnsuch that Av=位惫, for some scalar 位.

02

Check whether v⇀ is aneigen vector of A+2In

Ifv鈬赌is an Eigen vector of A this means that:

If we now look atA+2In we will have:

A+2Inv鈬赌=Av鈬赌+2Inv鈬赌=位v鈬赌+2v鈬赌=位+2v鈬赌

Thus, v鈬赌is an Eigen vector of A+2Inwith Eigen valueAv鈬赌=位v鈬赌位+2 .

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