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Exercise 3

Avg difficulty 3.0

Decide which of these matrices are nilpotent.

  • (a)  (−24−12)\begin{pmatrix}-2&4\\ -1&2\end{pmatrix}     (b)  (3113)\begin{pmatrix}3&1\\ 1&3\end{pmatrix}     (c)  (−321−321−321)\begin{pmatrix}-3&2&1\\ -3&2&1\\ -3&2&1\end{pmatrix}     (d)  (11430−1527)\begin{pmatrix}1&1&4\\ 3&0&-1\\ 5&2&7\end{pmatrix}     (e)  (45−22−1933−16−1469−34−29)\begin{pmatrix}45&-22&-19\\ 33&-16&-14\\ 69&-34&-29\end{pmatrix}

Hefferon, Linear Algebra, Similarity, Strings, Exercise 3

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Adapted from Linear Algebra © 2016 Jim Hefferon. Licensed under CC BY-SA 3.0 US. Source: Linear Algebra. Imported at revision df2262e.