MATH 240 Final: MATH240 BOYLE-M SPRING2013 0101 FINAL SOL

• School: University of Maryland
• Department: Mathematics
• Course: MATH 240
• Professor: All

Document Summary

Math 240 spring 2013 final exam solutions. You may assume given matrix equations are well de ned (i. e. the matrix sizes are compatible): (a) (25 points) the following matrices are row equivalent: 0 (a) [7 pts] write down a basis for the row space of w . The rst three rows of r (not w ) are a basis for the row space of w . (b) [7 pts] write down a basis for the column space of w . The rst three columns of w (not r) are a basis for the row space of w . (c) [8 pts] write down a basis for the null space of w . No justi cation required: the set of vectors (x1, x2, x3) in r3 such that x1x2x3 = 0 is a subspace of r3. False: the set of polynomials {p1, p2, p3, p4} = {2+t, 3t+t2, 7+t+4t2, 1+9t+8t2} is linearly independent.