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Chapter 7: Q13E (page 336)

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]

Short Answer

Expert verified

Eigenvalues are:

位1=1,almu(1)=1

Step by step solution

01

Eigenvalues

  • In linear algebra, an eigenvector or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by 位, is the factor by which the eigenvector is scaled.
  • Eigenvalues of a triangular matrix are its diagonal matrix.
02

Step 2: Finding all real eigenvalues, with their algebraic multiplicities

Since, given matrix is triangular its eigenvalues arethe entries on the main diagonal;

det(A-位l)=0-位100-位110-位=0-位3+1=0位-1-位2-位-1=0

位1=1,位2,3=1卤1-4-2=-1卤3i2

Hence, the answer is:位1=1,almu(1)=1

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Most popular questions from this chapter

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[1234]

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a. Use the geometric interpretation of this transformation as a reflection combined with scaling to find the eigenvaluesA.

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A=114[13-2-3-210-6-3-65]

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