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Chapter 7: Q45E (page 338)

Do there exist invertiblematrices A and B such thatAB-BA=A?Explain.

Short Answer

Expert verified

Matrices A and B.

A-5l=-1-5k43-512=4kk=124k=3

The required constant k = 3

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,

Matrices A and B:

Now,

If 5is an eigenvalue

Thendet(A-5l)=0鈫�1

A-5l=-1-5k43-5

Multiplication:

=-6k4-2det(A-5l)=12-4k=0

The value is zero.

02

divide the value

det(A-5l)=12-4k=012=4kk=124k=3

Hence, the required constantk=3

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