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Chapter 7: Q47E (page 338)

For which2脳2 matrices A does there exist a nonzero matrix M Such that AM=MD,whereD=[2003] Give your answer in terms of eigenvalues of A.

Short Answer

Expert verified

Answer in terms of eigenvalues of A.

AM=M2003M-V1V2

Any matrix A that has 2 and 3 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=2003

Now,

role="math" localid="1659587981628" AM=M2003M-V1V2M2003=2V13V2

02

Apply the equation

=AV1AV2=AM

Equation applies for any matrix A that has 2 and 3 as eigenvalues.

Hence,

Any matrix A that has2and3 as eigenvalues.

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Most popular questions from this chapter

For each of the matrices in Exercises 1 through 13, find all real eigenvalues, with their algebraic multiplicities. Show your work. Do not use technology.

[010001100]

Is v鈬赌an eigenvector ofA-1? If so, what is the eigenvalue?

If v鈬赌is an eigenvector of matrix A, show that is in the image of A.or in the kernel ofA.

Find a basis of the linear space Vof all2脳2matrices Afor which[1-3] is an eigenvector, and thus determine the dimension of V.

Find all the polynomials of degree 鈮�2[a polynomial of the formf(t)=a+bt+ct2] whose graph goes through the points (1,3) and (2,6) , such thatrole="math" localid="1659541039431" f'(1)=1[wheref'(1)denotes the derivative].
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