MAT188H1 Midterm: MAT188H1_20169_641483478557mat188tut7sol

• School: UTSG
• Department: Mathematics
• Course: MAT188H1
• Professor: All

Document Summary

Faculty of applied science & engineering, university of toronto. Recall that one reason for the word linear in linear mappings (transformations) is that they preserve. Here"s a geometric interpretation on why the linear in. Then t maps a line segment in rn to a line segment in rm or to a single point in rm. Then z = x + t(y x), t r is the vector equation of the line through x and y. The line segment joining x and y is the portion of the line corresponding to 0 t 1. The above theorem is useful in computing images of subsets of rn. Example: let s be the unit square in r2 with vertices x = (cid:20)0. T : r2 r2 be the linear transformation de ned by t (x) = ax where a = (cid:20)1 1. Find and sketch the image of s under t .