I am having a difficult time understanding where I went wrong with the following:
$$\begin{matrix}4x-y = 1 \\ 2x+3y = 3 \end{matrix} $$
$$\begin{matrix}4x-y = -3 \\ 2x+3y = 3 \end{matrix} $$
I found the inverse of the common coefficient matrix of the systems:
$$A^{-1} \begin{cases} \frac3{14}, \frac1{14} \\ \\ -\frac17, \frac27 \end{cases} $$
The issue is this question:
Find the solutions to the two systems by using the inverse, i.e. by evaluating $A^{-1}B$ where $B$ represents the right hand side (i.e. $B = \begin{bmatrix}1 \\ 3 \end{bmatrix}$ for system (a) and $B = \begin{bmatrix}-3 \\ 3 \end{bmatrix}$ for system (b)).
Now whatever I find for x and y for both solutions keep coming as wrong. I am thinking, I might of read the question wrongly….I am using the negative values to find the x and y. Not too sure how to go at this now…
Best Answer
$A^{-1} = \frac{1}{14}\begin{bmatrix} 3 & 1 \\ -2 & 4\end{bmatrix}$.
$A^{-1} \binom{1}{3} = \frac{1}{14} \binom{6}{10} = \frac{1}{7} \binom{3}{5}$.
$A^{-1} \binom{-3}{3} = \frac{1}{14} \binom{-6}{18} = \frac{1}{7} \binom{-3}{9}$.