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About LinkBacksThe point of intersection of the linesand
is
. Use a matrix method to find
.
Thanks
You need to apply row reduction methods to this matrix:Originally Posted by Stroodle
The point of intersection of the lines
Thanks
![\left[\begin{array}{cc|c}2&3&a\\1&-2&5\end{array}\right]\xrightarrow{R_1\leftrightarrow R_2}{}\left[\begin{array}{cc|c}1&-2&5\\2&3&a\end{array}\right]\xrightarrow{-2R_1+R_2\rightarrow R_2}{}\left[\begin{array}{cc|c}1&-2&5\\0&7&a-10\end{array}\right]](http://latex.codecogs.com/png.latex?\left[\begin{array}{cc|c}2&3&a\\1&-2&5\end{array}\right]\xrightarrow{R_1\leftrightarrow R_2}{}\left[\begin{array}{cc|c}1&-2&5\\2&3&a\end{array}\right]\xrightarrow{-2R_1+R_2\rightarrow R_2}{}\left[\begin{array}{cc|c}1&-2&5\\0&7&a-10\end{array}\right])
Since the intersection point is (2,1), its matrix representation would be, it follows that
and
However, if I solve the first equation for a, I get, but when I solve the second equation for a, I get
....
Did you copy the intersection pt correctly?
The problem is that the second line doesn't even pass through the point of intersection!
Basically I think the second equation should beand then as far as I can see a=7 is the answer, which makes sense given that if you plug (2,1) into the first line equation you get ... 7. No real need for matrices here I fear...
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