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Q55E

Expert-verifiedFound in: Page 1

Book edition
5th

Author(s)
David C. Lay, Steven R. Lay and Judi J. McDonald

Pages
483 pages

ISBN
978-03219822384

**If A** **is a ${\mathbf{2}}{\mathbf{\times}}{\mathbf{2}}$ ****matrix with eigenvalues 3 and 4 and if localid="1668109698541" $\overrightarrow{\mathbf{u}}$** **is a unit eigenvector of A****, then the length of vector Alocalid="1668109419151" $\overrightarrow{\mathbf{u}}$** **cannot exceed 4.**

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

**The dedication of a system's eigenvalues and eigenvectors is vital in physics and engineering, in which it's far corresponding 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. **

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 difference among left and proper for eigenvalues).

Let be a unit eigenvector of A.

If its corresponding eigenvalue is 3.

Then,

$||Au||=||3u||=3\le 4$.

If the corresponding eigenvalue is though,

Then,

$||Au||=||4u||=4\le 4$ .

Therefore, the given statement is True.

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