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Chapter 7: Q34E (page 383)

If two 3脳3 matrices A and B both have the eigenvalues 1, 2, and 3, then A must be similar to B.

Short Answer

Expert verified

It is True that, If two 3脳3 matrices A and B both have the eigenvalues 1, 2, and 3, then A must be similar to B.

Step by step solution

01

Define eigenvalue:

Eigenvalues are a set of specialized scales associated with a system of linear equations. The corresponding eigenvalue, often denoted by 位.

02

Explanation for eigenvalues:

These two matrices, A and B are both 3脳3matrices with the exact same three distinct eigenvalues, 位1=1,位2=2and位3=3, so both of them have the same diagonalization,

D=100020003

Thus, A and B are similar.

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Most popular questions from this chapter

Arguing geometrically, find all eigenvectors and eigenvalues of the linear transformations in Exercises 15 through 22. In each case, find an eigenbasis if you can, and thus determine whether the given transformation is diagonalizable.

Reflection about a line L inR2.

Find a 2脳2matrix A such that [31]and [12] are eigenvectors of A , with eigenvalues 5 and 10 , respectively.

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[-3040-10-273]

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find an eigenbasis for the given matrice and diagonalize:

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representing the orthogonal projection onto a plane E.
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