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Chapter 7: Q27E (page 345)

Consider a 2 脳 2 matrix A. Suppose that tr A = 5 and det A = 6. Find the eigenvalues of A.

Short Answer

Expert verified

The eigenvalues of A位1=2,位2=3

Step by step solution

01

Using Trace of A and Det(A)

Consider a 2 x 2 matrix with values a,b,c,d for reference.

A=abcd

We have

Tr(A)= a + d = 5

det(A)= ad 鈥� bc = 6.

02

Finding eigen values using det(A-λl)=0

Equating the known(matrix) and unknown (eigen values) values in detA-位濒=0

a-位bCd-位=0

role="math" localid="1659593736662" a-位(d-位)-bc=0位2-a+d位+(ad-bc)=0位2-5+6=0位-2位-3=0位1=2,位2=3

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Most popular questions from this chapter

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