opatovaL
2021-09-16
Answered

Prove or disprove that if a and b are rational numbers, then $a}^{b$ is also rational.

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aprovard

Answered 2021-09-17
Author has **94** answers

Given statement: If a and b are rational numbers, then

The given statement is false, which will be disproven using a counterexample.

Counterexample

If

Result:

Statement is false, one counterexample is for a=-1 and

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I know i have to find the eigenvalues and eigenvectors of the matrix $A=\left(\begin{array}{cc}1& 1\\ 0& 1\end{array}\right)$

there's only one eigenvalue which is 1 and only "one" eigenvector and we can choose $\left(\begin{array}{c}1\\ 0\end{array}\right)$

but now I dont know what to do.

what comes next?

I know i have to find the eigenvalues and eigenvectors of the matrix $A=\left(\begin{array}{cc}1& 1\\ 0& 1\end{array}\right)$

there's only one eigenvalue which is 1 and only "one" eigenvector and we can choose $\left(\begin{array}{c}1\\ 0\end{array}\right)$

but now I dont know what to do.

what comes next?

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