I think that the absolute value of the determinant is the enlargement factor of a matrix. So if ad-bc is 2.2-0.0 the factor is 4. Is that correct?
A question says "Obtain the 2 × 2 matrix M associated with an enlargement, scale factor 2." I think that the a and d elements must be the square root of 2. Why does the answer say they are 2?
You are mistaken.
The determinant of a matrix gives you the area represented by the matrix, not the scale factor of enlargement. An enlargement of scale factor M is defined as
This can be shown quite easily. Take a general point x,y.
Now apply the transformation:
Edit: Was beaten by HallsofIvy
Really? 'Scale factor of enlargement' and 'enlargement factor' seem relatively interchangable to me. That's just personal opinion though. The determinant of a matrix just tells you the area. It doesn't tell you anything at all regarding the enlargement or transformation. Also, they asked you for a matrix, so clearly they didn't want you to calculate a determinant.
Ok, I think I see what you mean now, sorry. I still don't agree that it's an ambiguous question though. It specifically asks for a scale factor 2 enlargement - although the wording is slightly questionable, I think the meaning is quite easily interpreted. I can see why it would confuse you, but I have seen other exam questions that have been worded extremely similarly.