MATH115 Study Guide - Quiz Guide: Row And Column Spaces
2 Dec 2014
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2 (cid:1) sin(cid:0) 5 (cid:1) (cid:20) cos(cid:0) 5 (cid:1) (cid:21) sin(cid:0) 5 (cid:1) cos(cid:0) 5 (cid:21) (cid:20) 3 (cid:21) (cid:20) 1 (cid:21) (cid:20) 1. 2perp 3 (cid:21) (cid:20) 5 (cid:20) 12 5. Hence [g] = (c) [h] = [f ][g] = 3: {9 marks} the following matrix a has matrix r as its rref. Note: this also tells us that the 4 rows of a are linearly independent, so we could have also chosen the. 1: {3 marks} consider the mapping f : r3 r3 that maps a vector (cid:126)x to the point on the plane x1 + x2 + x3 = 1 closest to (cid:126)x. Explain why this is not a linear mapping. If f is linear, then f ((cid:126)0) = f ((cid:126)x (cid:126)x) = f ((cid:126)x) f ((cid:126)x) = (cid:126)0. In this example, f ((cid:126)0) lies on the plane x1 + x2 + x3 = 1, that does not contain the zero vector.
