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January 14th, 2019, 09:10 AM   #1
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Matrix

Hi all, can someone please tell me how they got this equation from this matrix. I seem to get two products with X2 instead of one.

Please see attachment.
Thank you!
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January 14th, 2019, 12:50 PM   #2
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The right side should be a 2-vector. You should end up with two equations.
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January 14th, 2019, 02:21 PM   #3
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Math Focus: Wibbly wobbly timey-wimey stuff.
This becomes:
$\displaystyle \left ( \begin{matrix} 106.67 \times 10^3 - 129.5439 \times 300 & -53.34 \times 10^3 \\ -53.34 \times 10^3 & 106.67 \times 10^3 -129.5439 \times 500 \end{matrix} \right ) \left ( \begin{matrix} 1 \\ x_2 \end{matrix} \right ) = \left ( \begin{matrix} 0 \\ 0 \end{matrix} \right )$

Does writing it like this help?

-Dan
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January 15th, 2019, 09:36 AM   #4
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It's easier to outline with letters.

$\displaystyle [ \begin{bmatrix}
a &b \\
-b & a
\end{bmatrix}+\begin{bmatrix}
c & 0\\
0& d
\end{bmatrix}] \begin{bmatrix}
1\\
x
\end{bmatrix}=\begin{bmatrix}
a+c &b \\
-b &a+d
\end{bmatrix}\begin{bmatrix}
1\\x
\end{bmatrix}=0$
$\displaystyle (a+c)+bx=0$
$\displaystyle -b+(a+d)x=0$
$\displaystyle -\frac{a+c}{b}=\frac{b}{a+d}$
This is the test for a solution. Now substitute numbers and if this equation is satisfied, you can solve for x which is probably the second equation of OP.
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