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What is the transformation matrix M that transforms a square in the x-y plane defined by (1, 1)T (-1, 1)T (-1, -1)T (1, -1)T to a parallelogram whose corresponding vertices are (2, 1)T (0,1)T (-2, -1)T and (0, -1)T ? Following are options below. This is not a homework question.

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I can easily find transformation matrix in 2X2 but how 3X3 ? I got confused between Option A and C. How third row and column is added ?

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    $\begingroup$ The 2x2 upper left matrix is a skew in both A and C, the third column adds a translation. In A the translation is 0,0 and in C the translation is 1,0. $\endgroup$
    – pmw1234
    Commented Jul 30, 2023 at 11:01
  • $\begingroup$ So, out of A and C, which one is correct ? and Why ? $\endgroup$
    – Rajesh Prajapati
    Commented Jul 30, 2023 at 11:29
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    $\begingroup$ I think the entire point of this question is to get the reader to recognize that a 2x2 matrix can be pulled out and multiplied by the points. Doing that to just 1 point will yield the correct answer since that point with either need to be translated(C) or left as is(A). I highly recommend going through the exercise of multiplying the 2x2 matrix by the first point to get the answer to the question. $\endgroup$
    – pmw1234
    Commented Jul 30, 2023 at 12:16

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