235HW2 - Math 235: Linear Algebra HW 2 Problem 1.4.1...

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Unformatted text preview: Math 235: Linear Algebra HW 2 Problem 1.4.1 Problem 1.4.1 Find all solutions to the following system of equations by row-reducing the coefficient matrix: 1 3 x 1 + 2 x 2- 6 x 3 = 0- 4 x 1 + 5 x 3 = 0- 3 x 1 + 6 x 2- 13 x 3 = 0- 7 3 x 1 + 2 x 2- 8 3 x 3 = 0 1 3 2- 6- 4 5- 3 6- 13- 7 3 2- 8 3 1 6- 18- 4 0 5- 3 6- 13- 7 6- 8 1 6- 18 0 24- 67 0 24- 67 0 48- 134 1 6- 18 0 24- 67 1 6- 18 0 1- 67 24 0 0 0 0 1 0- 5 4 0 1- 67 24 0 0 0 0 So we know that for any element c R that we can have: x 1 = 5 4 c , x 2 = 24 67 c , and x 3 = c Problem 1.4.5 Give an example of a system of equations in two unknowns which has no solution. This can only happen in the following way: ax + by = r cax + cay = s Looking at the coefficient matrix we see: a b r ca cb s a b r s- cr So if s- cr 6 = 0 then the system of equations has no solution.= 0 then the system of equations has no solution....
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This note was uploaded on 11/14/2010 for the course PHYCS 498 taught by Professor Aa during the Spring '10 term at University of Illinois, Urbana Champaign.

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235HW2 - Math 235: Linear Algebra HW 2 Problem 1.4.1...

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