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


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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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You need to solve the linear system which you have for $x$ and $y$. This will give you the equation of a line in $2D$ (barring calculation errors). – Daryl Oct 22 '12 at 4:30
Not really sure how to get there, should I convert to y=mx+c? – JackyBoi Oct 22 '12 at 5:02
up vote 0 down vote accepted

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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so the gradient m = $3.526 / 18$ ? – JackyBoi Oct 22 '12 at 10:05
I reckon that is correct. Do you understand the process? – Daryl Oct 22 '12 at 12:05
except the part why the bottom ones are 0's? I understand the top part – JackyBoi Oct 22 '12 at 15:38
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. – Daryl Oct 22 '12 at 21:48

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