Homework #2 for Math H110, fall '02
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1. Show that the kernel of a linear transformation is a subspace.
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2. Let T:V->W, and S:W->X. Find good bases of V,W,X so that each of
T, S, and S o T all look nice. (Part of the problem is to decide
what "nice" could mean.)
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3. Show that any finite field has #elements = a power of a prime.
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4. Show any 2x2 invertible is (uniquely) the product of an orthogonal matrix,
a diagonal matrix with positive real entries, and a shear matrix
(upper triangular with ones on the diagonal).
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5. Curtis 2.7 #4,6