Solve for x and y:

Question:

Solve for x and y:

$x\left[\begin{array}{l}2 \\ 1\end{array}\right]+y\left[\begin{array}{l}3 \\ 5\end{array}\right]+\left[\begin{array}{c}-8 \\ -11\end{array}\right]=\mathrm{O}$

Solution:

Given, $x\left[\begin{array}{l}2 \\ 1\end{array}\right]+y\left[\begin{array}{l}3 \\ 5\end{array}\right]+\left[\begin{array}{c}-8 \\ -11\end{array}\right]=O$

$\left[\begin{array}{c}2 x \\ x\end{array}\right]+\left[\begin{array}{c}3 y \\ 5 y\end{array}\right]+\left[\begin{array}{c}-8 \\ -11\end{array}\right]=O$ (Multiplying the variables with the matrices)

So, $\left[\begin{array}{c}2 x+3 y-8 \\ x+5 y-11\end{array}\right]=\left[\begin{array}{l}0 \\ 0\end{array}\right]$ (Addition of matrices)

Now, we have

2x + 3y – 8 = 0 ….. (1) and

x + 5y – 11 = 0 ….. (2)

On solving the equations (1) and (2), we get

x = 1 and y = 2

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