Q29E There exists a positive integer ... [FREE SOLUTION]

91影视

Linear Algebra With Applications

Otto Bretscher

$Math Studyset 91影视 Explanations$ Math

5th Edition 路 442 pages

ISBN: 9780321796974

Chapter 2: Q29E (page 108)

There exists a positive integer n such that ${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{n} = l_{2}$ .

Short Answer

Expert verified

The statement is true.

Step by step solution

Explaining

The claim is that there exists a positive n such that ${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{n} = l_{2}$ . First, we will calculate the following and look for a pattern:

${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{2} = [\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}] {[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{3} = [\begin{matrix} - 1 & 0 \\ 0 & - 1 \end{matrix}] [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] = [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}]$

Conclusion

${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{4} = [\begin{matrix} 0 & 1 \\ - 1 & 0 \end{matrix}] [\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}] = [\begin{matrix} 1 & 0 \\ 0 & 1 \end{matrix}]$

Thus we can see that ${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{4} = l_{2}$ the statement is true.

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91影视

There exists a positive integer n such that ${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{n} = l_{2}$ .

Short Answer

Step by step solution

Explaining

Conclusion

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91影视

There exists a positive integer n such that [0-110]n=l2.

Short Answer

Step by step solution

Explaining

Conclusion

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There exists a positive integer n such that ${[\begin{matrix} 0 & - 1 \\ 1 & 0 \end{matrix}]}^{n} = l_{2}$ .