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jenyasd209 [6]
3 years ago
9

Write the system of equations represented by the following matrices and matrix equation

Mathematics
1 answer:
MaRussiya [10]3 years ago
8 0
We have:

A=\left[\begin{array}{cc}3&-5\\4&1\end{array}\right]\qquad X=\left[\begin{array}{c}a\\b\end{array}\right]\qquad C=\left[\begin{array}{c}2\\10\end{array}\right]

so:

A\cdot X=C\\\\\\
\left[\begin{array}{cc}3&-5\\4&1\end{array}\right]\cdot\left[\begin{array}{c}a\\b\end{array}\right]=\left[\begin{array}{c}2\\10\end{array}\right]\\\\\\
\left[\begin{array}{c}3a-5b\\4a+1b\end{array}\right]=\left[\begin{array}{c}2\\10\end{array}\right]\\\\\\
\boxed{\begin{cases}3a-5b=2\\4a+b=10\end{cases}}

And the solution of the system of equations:

\begin{cases}3a-5b=2\\4a+b=10\quad|\cdot5\end{cases}\\\\\\
\begin{cases}3a-5b=2\\20a+5b=50\end{cases}\\---------(+)\\\\3a-5b+20a+5b=2+50\\\\3a+20a=52\\\\23a=52\quad|:23\\\\\boxed{a=\dfrac{52}{23}=2\dfrac{6}{23}}\\\\\\
4a+b=10\\\\b=10-4a\\\\b=10-4\cdot\dfrac{52}{23}\\\\\\b=\dfrac{230}{23}-\dfrac{208}{23}\\\\\\\boxed{b=\dfrac{22}{23}}\\\\\\
\boxed{\begin{cases}a=2\dfrac{6}{23}\\\\b=\dfrac{22}{23}\end{cases}}
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