MATH 235 Midterm: MATH 235 UMass Amherst midterm2-sec1
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Fall 2000: (18 points) you are given below the matrix a together with its row reduced echelon form b (you need not verify that b is indeed the reduced echelon form of a) Justify your answer carefully! (either explain why they are equal, or nd a vector in one that does not belong to the other): (16 points) let i = (cid:18) 1 0. 0 1 (cid:19) be the 2 2 identity matrix and a = (cid:18) 0 6: show that the matrix a 5i is invertible. Find these values of t: (18 points) determine if the following set in rn is a subspace. If it is not, nd a property in the de nition of a subspace which this set violates. Nd a matrix a such that this set is either n ull(a) or col(a). are real numbers satisfying. = 6 x + z such that a, b, c, d are arbitrary real numbers x y z.
