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1.  Prove that the linear transformation represented by the matrix M is rigid if and only if MT = M−1.

2.  Show that the linear transformation represented by the matrix M is orientation-preserving if and only if det (M) > 0.[

3.  Figure II.9 shows an affine transformation acting on an F.

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(a) Is this a linear transformation? Why or why not?

(b) Give a 3 × 3 matrix that represents the affine transformation.