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Chapter 7: Q17E (page 336)

Consider the matrix A=|abb-a|where aand bare arbitrary constants. Find all eigenvalues of A. Explain in terms of the geometric interpretation of the linear transformationT(x)鈫�=Ax鈫�.

Short Answer

Expert verified

Eigenvalue ofA=位1,2=卤a2+b2

Step by step solution

01

Eigenvalues

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by , is the factor by which the eigenvector is scaled.

02

Step 2: Find all eigenvalues of A

We can clearly see that,

detA-位l=0a-位bb-a-位=0位2-a2-b2=0位1,2=4a2+b22=卤a2+b2

Hence,位1,2=卤a2+b2.

In terms of transformationL=2ab

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