According to Exercise 7.3.9. any (n + 1) x (n + 1) matrix of the block form
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in which A is an n x n matrix and b Rn can be identified with the affine transformation F[x] = Ax + a on Rn. Exercise 9.4.46 shows that every matrix in the one-parameter group etB generated by
has such a form, and hence we can identify etB as a family of affine maps on Describe the affine transformations of generated by the following matrices:
(a)
(b)
(c)
(d)
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