MATH 221 Study Guide - Midterm Guide: Symmetric Matrix, Row Echelon Form, Horse Length

• School: UBC
• Department: Mathematics
• Course: MATH 221
• Professor: All

Document Summary

The rst 9 problems are common to all three sections, the last problem is section-speci c. Your answer will depend on k. x1 + x2 2x3 + x4 = 1. 2x1 + 2x2 3x3 + x4 = 2. 3x1 + 3x2 4x3 + x4 = k. Let u = (1, 2, 1), v = ( 1, 0, 1), w = (2, 3, 2) be three vectors in r3. Let l : r2 r2 de ned by l(cid:18)(cid:20)x y(cid:21)(cid:19) = (cid:20) x y x(cid:21). 1 (cid:21)(cid:27) be a basis of r2. (a) find the representation of l with respect to the basis t . (b) let v be a vector in r2 such that [l(v)]t = (cid:20) 1. Let l : r3 r3 be a linear transformation for which we know that. 3 (b) find the matrix a of l with respect to the standard basis. (c) find det(a). Suppose that the echelon form of a is given by.