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Chapter 7: Q49E (page 338)

For which3脳3 matrices A does there exist a nonzero matrix M Such that AM=MD,where D=[200030004]Give your answer in terms of eigenvalues of A.

Short Answer

Expert verified

D=200030004AM=M200030004

Any invertible matrix A that has 2,3,4 as eigenvalues.

Step by step solution

01

definition of matrix

A function is defined as a relationship between a set of inputs that each have one output.

Given,

D=200030004AM=M200030004

Then,

M=V1V2V3M=2003

02

Multiply

If

M=2003=2V13V2AV3=AV1AV2AV3=AM

So, the given equation applies for any invertible matrix A that has 2,3,4 as eigenvalues.

Hence,

Any invertible matrix A that has 2,3,4 as eigenvalues.

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