For the matrices below. Find all (real) eigenvalues. A= [7 9] [0 9]

Question

For the matrices below. Find all (real) eigenvalues.

A= [7 9]
[0 9]

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Thái Dương 5 years 2021-08-30T00:56:13+00:00 1 Answers 21 views 0

Answers ( )

  1. Latifah
    0
    2021-08-30T00:58:05+00:00
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    Answer:

    The answer is “9 and 7“.

    Step-by-step explanation:

    Given:

    A=\left[\begin{array}{cc}7&9\\0&9\end{array}\right]

    Using formula:

    |A-\lambda \cdot I|= 0\\\\

    \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]-\lambda \left[\begin{array}{cc}1&0\\0&1\end{array}\right] |=0\\\\\\ \to |\left[\begin{array}{cc}7&9\\0&9\end{array}\right]- \left[\begin{array}{cc}\lambda&0\\0&\lambda\end{array}\right] |=0\\\\\\\to|\left[\begin{array}{cc}7-\lambda &9\\0&9-\lambda\end{array}\right]|=0\\\\\\\to|(7-\lambda)(9-\lambda)|=0\\\\\to (7-\lambda)(9-\lambda)=0\\\\\to 7-\lambda=0 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 9-\lambda=0\\\\

    \to \lambda=7 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \lambda=9\\\\

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