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Solve for x and y:
\mathrm{x}\left[\begin{array}{l} 2 \\ 1 \end{array}\right]+\mathrm{y}\left[\begin{array}{l} 3 \\ 5 \end{array}\right]+\left[\begin{array}{c} -8 \\ -11 \end{array}\right]=0

Answers (1)

We are given with the following matrix equation,

x\left[\begin{array}{l}2 \\ 1\end{array}\right]+y\left[\begin{array}{l}3 \\ 5\end{array}\right]+\left[\begin{array}{l}-8 \\ -11\end{array}\right]=0
We need to find x and y 
 \\x\left[\begin{array}{l}2 \\ 1\end{array}\right]+y\left[\begin{array}{l}3 \\ 5\end{array}\right]+\left[\begin{array}{l}-8 \\ -11\end{array}\right]=0 \\ \Rightarrow\left[\begin{array}{l}2 \mathrm{x} \\ \mathrm{x}\end{array}\right]+\left[\begin{array}{l}3 \mathrm{y} \\ 5 \mathrm{y}\end{array}\right]+\left[\begin{array}{c}-8 \\ -11\end{array}\right]=0
These matrices can be added easily as they are of same order.
\Rightarrow\left[\begin{array}{l}2 x+3 y-8 \\ x+5 y-11\end{array}\right]=\left[\begin{array}{l}0 \\ 0\end{array}\right]

If two matrices are equal, then their corresponding elements of the same matrices are also equal.

This implies,

\\2x + 3y - 8 = 0 $ \ldots $ (i) \\x + 5y - 11 = 0 $ \ldots $ (ii)

We have two variables, x and y; and two equations. It can be solved.

By rearranging equation (i), we get

2x + 3y = 8 $ \ldots $ (iii)

By rearranging equation (ii), then multiplying it by 2 on both sides, we get

 \\x + 5y = 11 \\2(x + 5y) = 2 \times 11 \\ \Rightarrow 2x + 10y = 22 \ldots (iv)

By subtracting equation (iii) from (iv), we get

 \\(2x + 10y) - (2x + 3y) = 22 - 8 \\ \Rightarrow 2x + 10y - 2x - 3y = 14 \\ \Rightarrow 2x - 2x + 10y - 3y = 14 \\ \Rightarrow 7y = 14

\\ \Rightarrow y = 2

By substituting y = 2 in equation (iii), we get

\\2x + 3(2) = 8 \\ \Rightarrow 2x + 6 = 8 \\ \Rightarrow 2x = 8 - 6 \\ \Rightarrow 2x = 2

\Rightarrow x = 1

Thus, x = 1 and y = 2

 

Posted by

infoexpert22

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