MATH 551 Midterm: MATH 551 KSU Test2 S15
15 Feb 2019
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You must show your work clearly and in order to receive credit. Problem 1 [10 points] (a) write a generic linear combination of v1 = unknowns x1, x2. Using (b) set a generic combination of v1 and v2 equal to b1 = as a linear combination of v1 and v2. Then write b1 (c) determine whether b2 = . Problem 2 [10 points] consider the subspace s = span{v1, v2, v3, v4} of r3 where v1 = . 3 (a) find which vi"s are redundant for s and explain why. (b) explain how a basis for s can be found and compute its dimension. Problem 3 [10 points] write the de nition of the null space for the matrix a. Then explain and justify how one can nd a basis for null(a). Problem 4 [10 points] consider two bases c and b of r2 and a vector v r2: Problem 5 [10 points] find the lu-factorization of the matrix:
