MATH 235 Midterm: MATH 235 UMass Amherst midterm2-fall06-compact
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Fall 2006: (24 points) you are given below the matrix a together with its row reduced echelon form b. Use part b to justify your: (16 points) a) let a = (cid:20) 1 3. 2 5 (cid:21) and c = (cid:20) 1 2 1. Ab = c: check your answer in part a by calculating ab, a) (6 points) let a = (cid:18) 1. 2 1 (cid:19) , p = (cid:18) 1 2. 1 3 (cid:19) , and b a 2 2 matrix satisfying. Hint: first express b in terms of a and p . (check that your b satis es equation (1). : (10 points) let a = . Compute its inverse a 1. (check that: (18 points) determine which of the following sets in rn is a subspace. Nd a property in the de nition of a subspace which this set violates.
