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    The linear transformation T from R^3 to R^3 maps the points (1,0) and (1,1) to the points (-2,1) and (-1,1) respectively

    Find the 2x2 matrix M which represents T.
    Find M and describe T in words
    Find the cartesian of the image under T of the line y = x - 1
    Firstly, what's R^3?

    Now the rest is alright, apart from the last part.

    T ends up as

    1, -2
    0, 1

    Now that seems to be a shear parallel to the X axis.

    So for the last part

    (x,x-1) maps onto (2-x,x-1).

    How does I find the cartesian equation of the image of those mappings?
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    R^3, 3 dimensional space.
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    (Original post by JamesF)
    R^3, 3 dimensional space.
    Thought it might be, but surely this context we're talking R^2?
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    T(a,a-1)=(2-a,a-1)

    Doesn't the image thus have cartesian equ^n y=1-x ?
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    (Original post by DanielW3)
    T(a,a-1)=(2-a,a-1)

    Doesn't the image thus have cartesian equ^n y=1-x ?

    Yes. But why? It's not obvious to me.
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    (a,a-1) maps onto (2-a,a-1) so x = 2-a, y = a-1
    a = 2-x, a = 1+y
    2 - x = 1 + y
    y = 1 - x
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    (Original post by Bezza)
    (a,a-1) maps onto (2-a,a-1) so x = 2-a, y = a-1
    a = 2-x, a = 1+y
    2 - x = 1 + y
    y = 1 - x
    That's what I would've done
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    (Original post by fishpaste)
    Firstly, what's R^3?

    Now the rest is alright, apart from the last part.

    T ends up as

    1, -2
    0, 1

    Now that seems to be a shear parallel to the X axis.

    So for the last part

    (x,x-1) maps onto (2-x,x-1).

    How does I find the cartesian equation of the image of those mappings?
    That R^3 maps on to R^3 just means that a dimension isn't crushed in the transformation (ie the determinant of the matrix is not zero).

    The linear transformation T from R^3 to R^3 maps the points (1,0) and (1,1) to the points (-2,1) and (-1,1) respectively

    Find the 2x2 matrix M which represents T.
    Find M and describe T in words
    Find the cartesian of the image under T of the line y = x - 1

    The linear transformation T from R^3 to R^3 maps the points (1,0) and (1,1) to the points (-2,1) and (-1,1) respectively

    Find the 2x2 matrix M which represents T.
    Find M and describe T in words
    Find the cartesian of the image under T of the line y = x - 1

    Once you've found the matrix, you can always use matix algebra and a suitable parametric equation of the line (eg x=a, y=a-1) and then find what it maps to. You'll then get the parametric equation of the line, from which you can find the cartesian equation easily. (x=-a-1 and y=a, so a=-1-x and y=-1-x).
 
 
 
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