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.)

Reply 4

Sb22312

2

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!?

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.

Reply 6

pouii

OP

1

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

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.

(edited 7 years ago)

Reply 8

pouii

OP

1

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?

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.

(edited 7 years ago)

Reply 10

pouii

OP

1

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.