232sol3

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Unformatted text preview: nk. A1. We want to find the reduced row echelon form of The only situations where we did not get full rank were (i) a = b = 0 and (ii) a, b 6= 0, a = ±b. We can succinctly state both (i) and (ii) together by noting that together they cover precisely the situations when a = ±b. A2. (a) If our system has more variables than equations, then we have less rows in the augmented matrix than columns representing variables, so we will have at least one free variable. So if the system is consistent, we will have infinitely many solutions. This situation is possible, e.g., 1111 0012 we will have infinitely many solutions since the second variable is free and the system is consistent. But the system can also be inconsistent and so have no solutions, e.g., we could wind up with 1111 0002 C EDRIC C HAUVE , FALL 2013 1 f a cu lty of sc ie nce d ep ar tment of mathem atics Week Date Sections Part/ References MATH 895-4 Fall 2010 Course Schedule Topic/Sections MATH 232 A SSIGNMENT #3 Notes/Speaker from FS2009 So the exhaustive list of possible solution set sizes is {0, 1...
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This document was uploaded on 03/03/2014 for the course MATH 232 at Simon Fraser.

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