MATH-205 Midterm: Bates MATH 205 021805jayawant205exam
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Use properties of determinants to compute: (a) det a2b t (b) det 2b (c) det c where c is obtained from a by interchanging rows 2 and 4 (d) det (b 2) 1 if b 2 is invertible. Otherwise, explain why b 2 is not invertible: (8 points) let a = (cid:20) 2 4 2. 6 7 3 (cid:21). (a) find an lu factorization of a. (b) use the lu factorization in part (a) to solve the equation a~x = (cid:20) 1. 1 (cid:21): (8 points) let a = (cid:20) 2. Explain: (8 points) supose a 5 5 matrix a is invertible. A are linearly independent. (if you nd it helpful, you may use the following steps in your explanation. ) So the number of pivots in a is. Explain. (b) let w be the set of all polynomials of the form p(t) = t + a where a is a real number.
