MATH115 Study Guide - Quiz Guide: Gaussian Elimination, Burh, Elementary Matrix
2 Dec 2014
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Math 115 fall 2012 lab 5 solutions: {10 marks} let a = A 1 = (b) use part (a) to solve the system of linear equations with the following augmented matrix: This system a(cid:126)x = (cid:126)b has the solution. As a product of (ideally 3) elementary matrices. We can perform 3 eros to get from b to i: {6 marks} express b = The three eros correspond to the elementary matrices (in order) (cid:126)x = a 1(cid:126)b = This tells us that e3e2e1b = i, so b = e 1: {4 marks} other than the identity matrix, determine two possible 2 2 matrices a such that a = a 1. At least one of the two matrices must have all nonzero entries. (hint: think about geometric mappings and their standard matrices. ) We can quickly nd some diagonal matrices that satisfy a = a 1, such as (cid:20) 1.
