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Chapter 7: Q55E (page 325)

If Ais a2脳2matrix with eigenvalues 3 and 4 and ifu鈫�is a unit eigenvector ofA, then the length of vectorAu鈫�cannot exceed 4.

Short Answer

Expert verified

The given statement is True because, the given matrices are not exceeded 4.

Step by step solution

01

Definition of Eigenvalue

The dedication of a system's eigenvalues and eigenvectors is vital in physics and engineering, in whichit's farcorresponding to matrix diagonalization and takes place in programs as various as balance analysis, rotating frame physics, and tiny oscillations of vibrating systems, to say a few.

02

Determine whether the given statement is true or false

Each eigenvalue has an eigenvector that corresponds to it (or, in general, a corresponding proper eigenvector and a corresponding left eigenvector; there may be no analogous differenceamong left and proper for eigenvalues).

Letu be a unit eigenvector of A .

If its corresponding eigenvalue is 3 .

Then,

Au=3u=3猢�4.

If the corresponding eigenvalue is 4 though,

Then,

.Au=4u=4猢�4

Therefore, the given statement is True.

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Most popular questions from this chapter

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14.(100-500001)

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.
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