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# The 2nd FP1 paper i'm doing

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1. http://files.physicsandmathstutor.co...%20Edexcel.pdf

I don't quite understand how to do part c, can someone explain what's going on?
2. (Original post by pouii)
http://files.physicsandmathstutor.co...%20Edexcel.pdf

I don't quite understand how to do part c, can someone explain what's going on?
What question?
3. (Original post by RDKGames)
What question?
oops question 2
4. (Original post by pouii)
oops question 2
Find the area of the initial rectangle, then find what the multiplier is between the initial area and the area after it is transformed.

det(A) should be equal to this because the determinant tells you the area multiplier for a particular matrix (not particularly happy with my explanation but I can't think of it differently to explain. I'm sure you know what I mean.)
5. The determinant shows the scale factor for enlargement so find the original area of the rectangle the det is a+4 . Area of shape orgianly is 2 . So 9 is how much been enlarged so 9=a+4 so a=5. Hope that's ok!?
6. (Original post by Sb22312)
The determinant shows the scale factor for enlargement so find the original area of the rectangle the det is a+4 . Area of shape orgianly is 2 . So 9 is how much been enlarged so 9=a+4 so a=5. Hope that's ok!?
Let's not post full solutions.
7. (Original post by RDKGames)
Find the area of the initial rectangle, then find what the multiplier is between the initial area and the area after it is transformed.

det(A) should be equal to this because the determinant tells you the area multiplier for a particular matrix (not particularly happy with my explanation but I can't think of it differently to explain. I'm sure you know what I mean.)
Well obviously the area of the rectangle is 2 and 18/2 is 9
but here in bold is what i don't understand what you've done

(Original post by Sb22312)
The determinant shows the scale factor for enlargement so find the original area of the rectangle the det is a+4 . Area of shape orgianly is 2 . So 9 is how much been enlarged so 9=a+4 so a=5. Hope that's ok!?
so good that i've understood everything you've done there
8. (Original post by pouii)
Well obviously the area of the rectangle is 2 and 18/2 is 9
but here in bold is what i don't understand what you've done

so good that i've understood everything you've done there
Well it should've made sense if you understand what the determinant actually means. Consider what the determinant tells you about the area within a 2x2 matrix and then it'll make sense. I meant the area scale factor when I said multiplier.
9. (Original post by RDKGames)
Well it should've made sense if you understand what the determinant actually means. Consider what the determinant tells you about the area within a 2x2 matrix and then it'll make sense. I meant the area scale factor when I said multiplier.
Well the determinant can tell me whether a matrix is singular or not. If the matrix has a determinant=0 then that matrix is singular and has no inverse.

but how does this help me?
10. (Original post by pouii)
Well the determinant can tell me whether a matrix is singular or not. If the matrix has a determinant=0 then that matrix is singular and has no inverse.

but how does this help me?
That's not the only thing determinants tell you. If it's 0 then the matrix is singular hence no inverse; yes that is true. In addition, if the matrix does not equal 0, then the number we get is the area scale factor (only for 2x2, it would be volume scale factor for 3x3) of any 2D object you apply that matrix to. So the area of the original object multiplied by the determinant will give you the area of it after it has been transformed by that particular matrix. So really, all you would've done for that part is say 2(a+4)=18 and then solve for a.

Also, if the determinant is negative, then we are told that the matrix involves a reflection of the object at some point.
11. (Original post by RDKGames)
That's not the only thing determinants tell you. If it's 0 then the matrix is singular hence no inverse; yes that is true. In addition, if the matrix does not equal 0, then the number we get is the area scale factor (only for 2x2, it would be volume scale factor for 3x3) of any 2D object you apply that matrix to. So the area of the original object multiplied by the determinant will give you the area of it after it has been transformed by that particular matrix. So really, all you would've done for that part is say 2(a+4)=18 and then solve for a.

Also, if the determinant is negative, then we are told that the matrix involves a reflection of the object at some point.
OH! I see
so area(1) x det = area(2)

but what if it gives me a negative det and area of original shape and asks me to get area of transformed shape?
12. (Original post by pouii)
OH! I see
so area(1) x det = area(2)

but what if it gives me a negative det and area of original shape and asks me to get area of transformed shape?
Take the magnitude, the negative sign indicates that there has been a reflection of the shape under the transformation matrix.
13. (Original post by B_9710)
Take the magnitude, the negative sign indicates that there has been a reflection of the shape under the transformation matrix.
oh ok thanks

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