MATH-205 Midterm: Bates MATH 205 021309ross205exam
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Label the columns of a as c1, c2, . Is the set s = {c1, c2, . Explain in terms of the de nition of linear independence. Write c3 as a linear combination of the other columns of a, or explain why this cannot be done. Write c4 as a linear combination of the other columns of a, or explain why this cannot be done. Show how to express b as a linear combination of all p columns of a in such a way that none of the weights involved are 0. 02/13/09: suppose t : ra rz is a transformation. Give the de nitions of each of the following: Suppose t : r3 r4 is de ned by t x1 x2 x3 x2x3 + 2x1. 2x2 + 7 a linear transformation and that it actually fails both parts of the de nition in (2a).
