MATH 551 Final: MATH 551 KSU Final Exam S15
15 Feb 2019
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You must show your work clearly and in order to receive credit. In particular, clearly indicate every row operation performed, and clearly answer the questions asked, in plain english. Problem 1 [10 points] show that the set of all vectors x = [x1 x2 x3 x4]t in r4 that satisfy the equations below is a subspace of r4. Also nd an orthonormal basis for it. (cid:26) x1 + x2 + x3. Problem 2 [10 points] to change coordinates from the standard basis to a new basis b = {v1, v2} of r2 one forms the matrix b = [v1 v2], and then solves the system b[v]b = v for [v]b. A linear transformation t represented by matrix multiplication by a, as in t (x) = ax, is represented by multiplication by a di erent matrix ab when using b-coordinates. To nd ab, write b[t (x)]b = ab[x]b, so that [t (x)]b = b 1ab[x]b.
