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Trying to find the gradient of the eigenline that is ofcourse finding the eigenvlaue, but stuck here

QUESTION:

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enter image description here

The matrix A has two eigenvalues h and k, where h > k. To 2 decimal places, what is the gradient of the eigenline that corresponds to eigenvalue h?

My Working: enter image description here

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    Not really sure how to get there, should I convert to y=mx+c?2012-10-22

1 Answers 1

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From the matrix equation, this system is row-equivalent to the system $\left[\begin{array}{cc|c}-3.526&-18&0\\0&0&0\end{array}\right],$ which is a consistent linear system. Performing back substitution gives $-3.526x+18y=0,$ which is the standard form for the equation of a line (equivalent to $y=\frac{3.526}{18}x$).

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    I performed the row operation $R_2\leftarrow R_2-\frac{5}{3.526}R_1$ as a part of the procedure of row reducing the matrix system.2012-10-22