MATH-205 Midterm: Bates MATH 205 021210ross205exam
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, let b = b1 b2 b3 and let c = . Find any/all conditions on b1, b2 and b3 which are necessary and su cient for b to be in the span of the set of column vectors of a. Give the correct de nition: what does it mean to say a set of vectors s = {v1, v2, . We say s is linearly independent if and only if. Explain in terms of the de nition of linear independence. Name: suppose t : rk rq is a transformation. De ne what it means for t to be a linear transformation: suppose t s1 s2 s3. 2 s2 s1 + s2 + s3(cid:21) is a transformation from r3 r2. Show t is not a linear transformation and in fact fails both parts of the de nition in problem (2). In your counterexamples" vectors, use all-di erent, positive, single digit numbers for the si"s.
