For which pairs of linear transformations in Exercise 1 is the composition S ◦ T defined?...

For which pairs of linear transformations in Exercise 1 is the composition S ◦ T defined? Calculate S ◦ T in these cases.

Exercise 1

Find the composition T ◦ S in each of the following.

(a)

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(b) S(x1 x2, x3) = (x1 + x3, x2, − x3 + x2); T(x1, x2, x3) = (x3, x1, x2)

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(c) S(x1, x2, x3, x4) = (x1 + x3 + x4, x1 − x2 − x3 + x4); T(x1, x2) = (6x1 − 7x2, 7x1 + 7x2)

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(d)