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    'Describe the geometrical transformation represented by the matrix:

    | 3 -4 | '
    | 4 3 |

    someone help me out with this please??? thought i understood matrix transformations but lol turns out not!

    im guessing theres a rotation and an enlargement but no clue how to get the actual values
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    (Original post by ithinkitslily)
    'Describe the geometrical transformation represented by the matrix:

    | 3 -4 | '
    | 4 3 |

    someone help me out with this please??? thought i understood matrix transformations but lol turns out not!

    im guessing theres a rotation and an enlargement but no clue how to get the actual values
    Begin by simply evaluating the determinant which should tell you whether or not there has been a reflection involved and it should lead you to the scale factor by which the transformation scales the plane.

    Once you have the scale factor, you can factor it out of the matrix and then recognise the rotation matrix thus find the angle by constructing equations in \theta
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    (Original post by RDKGames)
    Begin by simply evaluating the determinant which should tell you whether or not there has been a reflection involved and it should lead you to the scale factor by which the transformation scales the plane.

    Once you have the scale factor, you can factor it out of the matrix and then recognise the rotation matrix thus find the angle by constructing equations in \theta
    riiiight lol havent learnt about determinants yet which is probably why i couldnt do it! thanks anyway !
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    (Original post by ithinkitslily)
    riiiight lol havent learnt about determinants yet which is probably why i couldnt do it! thanks anyway !
    Ah okay, no worries then, there's an alternative which you might be a familiar with.

    For FP1 I found it useful to draw a diagram:
    Name:  Capture.PNG
Views: 28
Size:  26.1 KB

    Notice how the point (1,0) is moved to (3,4) and the point (0,1) \mapsto (-4,3)

    The value of h represents the scale factor. The angle \theta represents the rotation. You can work both of these out and discover what the components of the compound transformation are.

    It is often sufficient to do this with only 1 point, but to double check and ensure accuracy, the same transformations must apply to the second point so you can check whether the same transformation maps the second point to the correct location.
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    (Original post by RDKGames)
    Ah okay, no worries then, there's an alternative which you might be a familiar with.

    For FP1 I found it useful to draw a diagram:
    Name:  Capture.PNG
Views: 28
Size:  26.1 KB

    Notice how the point (1,0) is moved to (3,4) and the point (0,1) \mapsto (-4,3)

    The value of h represents the scale factor. The angle \theta represents the rotation. You can work both of these out and discover what the components of the compound transformation are.

    It is often sufficient to do this with only 1 point, but to double check and ensure accuracy, the same transformations must apply to the second point so you can check whether the same transformation maps the second point to the correct location.
    omg this is brilliant thank you!
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    (Original post by RDKGames)
    The value of h represents the scale factor. The angle \theta represents the rotation. You can work both of these out and discover what the components of the compound transformation are.
    I am somewhat uncomfortable with this repeated description of "the scale factor".

    Yes, if the transformation is the combination of a uniform scaling and a rotation, then we can extract a meaningful scale factor in a number of ways.

    But in general, the transformation will not cause uniform scaling - for example the transformation T = \begin{pmatrix}1 & 0 \\ 0 & 2 \end{pmatrix} scales the x-component by 1 and the y-component by 2. Moreover, for any S between 1 and 2 we can find a vector whose length is scaled by S when T is applied, and so talking about "the scale factor" as if there's a single value that must apply for every matrix is erroneous.

    I confess I don't know enough about what cases you might get asked in FP4 to know whether my concern is something the OP should worry about.
 
 
 
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