You have that
.
Now you need to find A such that
.
But
.
Therefore, A is the inverse of
.
Let B = {(1, -4), (-2, 9) and notice that B is a basis for R2. Therefore each (x,y) in R2 can be written as a linear combination of the vectors in B. If (x,y) = a(1,-4) + b(-2,9) then the coordinates of (x,y) relative to the basis B are said to be (a,b). (i.e. (x,y) = (a,b)B . Thus, associated with each (x,y) is another point in R2, (a,b). The function (sometimes called a transformation) that sends (x,y) to (a,b) is called a coordinate transformation. This transformation can be represented by a matrix. In other words, there is a matrix A such that the new coordinates (a,b) can be found by multiplying (x,y) on the left by A. Find A.
I have an answer but I'm not sure if I'm doing this right.