Scaling the image using Bilinear Interpolation

I have written a code that reads an image and does scaling of 2 units in x-axis direction. Scaling matrix is filled by values that are read from a text file.

Scaling Matrix looks like

2 0 0 
0 1 0 
0 0 1

Original Image

Transformed Image (Scaling of 2 units in X-direction)

Code

file = importdata('transform_c.txt');
fileData = file.data;
image = imread('mecca06.pgm');
[row, col] = size(image);
scalingMatrix = zeros(3,3);

scalingMatrix(1,1) = fileData(2);
scalingMatrix(1,2) = fileData(3);
scalingMatrix(1,3) = fileData(4);
scalingMatrix(2,1) = fileData(5);
scalingMatrix(2,2) = fileData(6);
scalingMatrix(2,3) = fileData(7);
scalingMatrix(3,1) = fileData(8);
scalingMatrix(3,2) = fileData(9);
scalingMatrix(3,3) = fileData(10);

m1Inverse = inv(scalingMatrix);

outputImage = applyTransformation(image, row, col, m1Inverse);
figure
imshow(outputImage);

function outImage = applyTransformation(image, row, col, m1Inverse)
    points = zeros(3,1);
    for i=1:row
        for j=1:col
            points(1,1) = i;
            points(2,1) = j;
            points(3,1) = 1;
            m2 = m1Inverse * points;

              x = m2(1,1);
              y = m2(2,1);
              xlb = floor(x);
              ylb = floor(y);

             if(xlb <= 0)
               xlb = 1;
             end

             if(xlb > row)
               xlb = row;
             end
             if(ylb <= 0)
               ylb = 1;
             end

             if(ylb > col)
               ylb = col;
             end

             xub = xlb+1;
             yub = ylb+1;

             if(xub <= 0)
                xub = 1;
             end

            if(xub > row)
               xub = row;
            end

            if(yub <= 0)
               yub = 1;
            end

            if(yub > col)
               yub = col;
            end

            exub = xub-x;
            eyub = yub-y;
            exlb = x-xlb;
            eylb = y-ylb;
            outImage(i,j) = (exub*eyub*image(xlb,ylb))+(exlb*eyub*image(xub,ylb))+(exub*eylb*image(xlb,yub))+(exlb*eylb*image(xub,yub));
          end
      end
  end

Question

When i apply the transformation, image is cropped. My question is how can i modify the above code to get uncropped image ?

I want to get the following image

[Rik]

You don't pre-allocate the result and you loop only over the size of the original.