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Chapter 7: Q41E (page 338)

If Matrix A is similar to B, show that tr B = tr AHint: Exercise 40is helpful.

Short Answer

Expert verified

If Matrix A is similar to B.

They A and B are similar matrices.

Then,

T-1AT=BtrB=tr(T-1AT)=tr(ATT-1)=trA

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,

Matrix A is similar to B.

They A and B are similar matrices.

Then,

T-1AT=B

02

definition of tr B = tr A

tr B equal the value of tr A

For an invertible T.

Now, using EX 40,

we compute .

trB=tr(T-1AT)=tr(ATT-1)=trA

Hence,

trB=tr(T-1AT)=tr(ATT-1)=trA

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Consider the matrix A=|abbc| where a, b, and c are nonzero constants. For which values of a, b, and c does A have two distinct eigenvalues?

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