# How do you solve Ax=B given A=((1, 5)) and B=(2)?

Nov 30, 2016

Solution is $x = \left(\begin{matrix}k \\ \frac{2 - k}{5}\end{matrix}\right)$

#### Explanation:

As $A = \left(\left(1 , 5\right)\right)$ is a $1 \times 2$ matrix and $B = \left(2\right)$ is a $1 \times 1$ matrix, as $A x = B$, $x = X$, where $X$ is a $2 \times 1$ matrix.

Let $x$ be $\left(\begin{matrix}{x}_{1} \\ {x}_{2}\end{matrix}\right)$

and hence $A x = \left(\left(1 , 5\right)\right) \left(\begin{matrix}{x}_{1} \\ {x}_{2}\end{matrix}\right) = \left({x}_{1} + 5 {x}_{2}\right)$

But as $A x = B = \left(2\right)$, we have ${x}_{1} + 5 {x}_{2} = 2$

or ${x}_{2} = \frac{2 - {x}_{1}}{5}$ and if ${x}_{1} = k$

Solution is $x = \left(\begin{matrix}k \\ \frac{2 - k}{5}\end{matrix}\right)$