MATH 271 Midterm: MATH 271 Amherst F15M271 2801 29Juul
15 Feb 2019
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December 21, 2015: (20 points) consider the matrix. Find the rank of t and the nullity of t : (15 points) let a, b, c r. show that b. 0 c c is not invertible: (10 points) let a be an n n matrix. 4 (a) find a basis for the null space of t . (b) find a basis for the range of t . (c) explain why your answers to parts (a) and (b) are consistent with the rank-nullity. 1: (15 points) for each of the following linear transformations, decide if t is an injection. Justify your answers. (a) t : p2 r3 is given by. T (p(x)) = (b) t : r4 m2 2, where t is not a surjection p( 1) p(0) p(1) (20 points) let v and w be two vector spaces and let t : v w be a linear. Suppose that s = {v1, v2, v3} is a subset of v such that.
