MATB24H3 Study Guide - Final Guide: Linear Map, Coordinate Vector
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Key words: isomorphism, invertible linear transformation, change of coordinate matrix. Relevant sections in the textbook:sec 3. 3, 3. 4, 7. 1 fb or 3c,3d sa. ~v w : let b be a an ordered basis for a vector space w . Give an isomorphism between w and rdim w. A: in class we said (or will say) a linear transformation respects the structure of a vector space, for instance it maps a subspace to a subspace, the zero vector to zero vector, and so on. In this question you investigate how a linear transformation treats a linear independent set and a spanning set. Let t : v f be a linear transformation, and suppose. Prove that t (i) is a linearly independent subset of w for every linearly independent subset i of v if and only if t is one to one. 2 (3) let t : v w be a linear transformation. Let s be a spanning set for v .
