MATH 1104 Lecture Notes - Lecture 1: Row Echelon Form, Jjy, Augmented Matrix

• School: Carleton University
• Department: Mathematics
• Course: MATH 1104
• Professor: Olga

Document Summary

Math1104 tutorial 1: for what value(s) of k is x1 x2 = 3k. 2x1 + 3x2 = k 2 consistent? (cid:34) Thus k can be any number: look at the following matrix: 1 h 1 1 0 1. Solution: 1) h = 1 2) h (cid:54)= 1; 3) no such h. For what values of h and k does the system have. Solution: 1) h = 12, k = 3; 2) h (cid:54)= 12; 3)h = 12, k (cid:54)= 3: given the relation (cid:126)u 2(cid:126)v 3 (cid:126)w = (cid:126)y, where (cid:34) Therefore, (cid:126)y can not be written as a linear combination of (cid:126)u, (cid:126)v, (cid:126)w. hence (cid:126)y (cid:54) span{(cid:126)u, (cid:126)v, (cid:126)w}: consider the following system of linear equations x1 + 4x2 8x3 = 0. Hence, for k (cid:54)= 9, the system has only trivial solution. (ii) solution: k = 9. (iii) when k = 9, from the discussion in (i), we have.