MATH 271 Midterm: MATH 271 Amherst F14M2712 28Dresch 29
15 Feb 2019
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Read this first: please read each question carefully. Final exam: true or false: (no justi cation necessary) (a) (b) (c) (d) (e) If a and b are n n matrices such that ab is the zero matrix, then a is the zero matrix or b is the zero matrix. If a is an invertible matrix then = 0 is an eigenvalue of a. If w is a subspace of r3, then dim w = 3 dim w . An eigenvalue has multiplicity (as a root of the characteristic equation) less than the dimension of the associated eigenspace. The range of a linear transformation is closed under addition and scalar multiplication. T f: suppose t : m2 2 m2 2 is the linear transformation whose matrix representation with re- spect to the basis b = (cid:26)(cid:20) 1 0. Find a basis for ker (t ). (c)
