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Chapter 7: Q10E (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.

[-3040-10-273]

Short Answer

Expert verified

Eigenvalues are:

位1,2=1,almu2=2位3=-1,almu1=1

Step by step solution

01

Eigenvalues

  • n 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: 

We can clearly see that,

detA-位滨=0-3-位040-1-位0-273-位=0-3-位-1-位3-位+8-1-位=0-1-位位2-1=0位1,2=0,位3=-1

Hence, the answer is:

位1,2=1,almu2=2位3=-1,almu1=1

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Most popular questions from this chapter

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