MAT224H1 Study Guide - Midterm Guide: Surjective Function
Document Summary
[4] 1(a) if t : v w is a linear transformation, then t carries linearly independent subsets of v onto linearly independent subsets of w . true false. The zero map is a linear transformation for any two vector spaces v and w , sending any vector in v to ~0 in w . Any subset of v gets send to the set {~0}, and this is not a linearly independent subset of w . [4] 1(b) if t : r2 r2 is a linear transformation, t (1, 0) = (1, 4), and t (1, 1) = (2, 5), then t is one-to-one. true false. We know that dim(r2) = 2 = dim(ker(t )) + dim(im(t )). Since (1, 4) and (2, 5) are linearly independent vectors, the image of t has at least dimension 2, and therefore, since it sits inside a 2-dimensional space, it is exactly 2.
