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Chapter 7: Q9E (page 323)

Find all2脳2matrices for whiche鈬赌1is an eigenvector.

Short Answer

Expert verified

So, the required matrix is 位b0d.

Step by step solution

01

Define the eigenvector

Eigenvector:An eigenvector ofAis a nonzero vector Vin鈩�nsuch thatAv=位v, for some scalar位.

02

Solve for

Ifv鈫�is an Eigen vector ofAthis means that:

Av鈫�=位'v

Now let A=abcd,v鈫�=10, and 位

We want to solve for A.

03

Evaluation

To do this we will replace everything into the equationAV鈫�=位v鈫�and

We will have:

Av鈫�=位v鈫�abcd10=位10a=位c=0

b,d are any real number

Thus, all matrices of the form 位b0dwill satisfy the given requirements.

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