Write the following in the form of AX = B Write the following system of equations in the form $AX = B$, and calculate the solution using the equation $X = A^{-1}B$.
$$2x - 3y = - 1$$
$$-5x +5y = 20$$
I'm not the strongest at linear algebra but I don't understand what the question is asking me over here or how to even go about solving this.
 A: Let $X = \left[\begin{matrix}x\\y\end{matrix}\right]$, then the first equation can be written, in matrix multiplication, as
$$\left[\begin{matrix}2&-3\end{matrix}\right]\left[\begin{matrix}x\\y\end{matrix}\right] = \left[\begin{matrix}-1\end{matrix}\right]$$
Similarly, the second equation can be written as
$$\left[\begin{matrix}-5&5\end{matrix}\right]\left[\begin{matrix}x\\y\end{matrix}\right] = \left[\begin{matrix}20\end{matrix}\right]$$
By combining these two equations as a system, they can be written as 
$$\begin{align*}\left[\begin{matrix}2&-3\\-5&5\end{matrix}\right]\left[\begin{matrix}x\\y\end{matrix}\right] &= \left[\begin{matrix}-1\\20\end{matrix}\right]\\
AX &= B
\end{align*}$$
Now, if the above $A$ has an inverse, then both sides can be left-multiplied by $A^{-1}$ to get
$$\begin{align*}AX &= B\\
A^{-1}AX &= A^{-1}B\\
I_2X &= A^{-1}B\\
X &= A^{-1}B\\
\left[\begin{matrix}x\\y\end{matrix}\right] &= \left[\begin{matrix}2&-3\\-5&5\end{matrix}\right]^{-1}\left[\begin{matrix}-1\\20\end{matrix}\right]
\end{align*}$$
And then the original unknowns in the system of equation can be solved.
A: HINT: You have a set of linear equations.
These can be written in Matrix form: $$AX=B$$
So you can build A by using the coefficients of x and y:
$$A=\begin{bmatrix}
  2 & -3 \\
  -5 & 5 \\
 \end{bmatrix}$$
X is the unknown variables x and y and it is a Vector:
$$X=\begin{bmatrix}
  x\\
  y\\
 \end{bmatrix}$$
And the multiplication of Matrix A with vector X is the solution vector B:
$$B=\begin{bmatrix}
  -1\\
  20\\
 \end{bmatrix}$$
To solve for X in linear algebra you cannot divide directly, but   accomplish this by taking the inverse of A and multiply it by B.
