This is actually easy to do:
You take T of the standard basis vectors and make the results the columns of a matrix A. (You must keep them in order- colm 1 must be T of the first basis vector, colm 2 the second, etc)
That will be the matrix that represents this transformation (that is, T(v) will equal Av - meaning taking T of a vector gives the same result as multiplying v on the left by A).
The standard basis vectors are (1,0) and (0,1)
T(1,0) = ( -4,2,0,1)
T(0,1) = (-9, -5, -3, 6)
Now let the matrix A be the 4x2 matrix with column 1 being (-4,2,0,1) and column 2 being (-9, -5, -3, 6)
(That is, A will have row 1 = [ -4 -9], row 2 will = [ 2 -5 ], etc.)
You can check this by taking some vector v and calculating T(v) and then Av and seeing you get the same result.
Also, if you let w be the vector (x1,x2) and calculate Aw you will see you get back the formula for the transformation. Note: this is how you find the transformation if you are only given it's matrix.
(of course, with the T form you input the vector as a row and you get out the answer as a row vector whereas with Av you put it in as a column vector and it gives it the answer as a column but it's the same result)