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Chapter 7: Q55E (page 384)

TRUE OR FALSE

If A is a 2 x 2matrix with eigenvalues 3 and 4 and if u鈫抜s a unit eigenvector of A, then the length of vector Au鈫� cannot exceed 4.

Short Answer

Expert verified

The given statement is True.

Step by step solution

01

Definition of Eigenvalue

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

02

Determine whether the given statement is true or false.

Let u be a unit eigenvector of A.

If its corresponding eigenvalue is 3. Then,

||Au|| = || 3u || = 3 鈮� 4

If the corresponding eigenvalue is 4 though. Then,

||Au|| = || 4u || = 4 鈮� 4

Therefore, the given statement is True.

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