mikeraj Posted October 31, 2016 Share Posted October 31, 2016 (edited) I have a question regarding one example of eigenvector calculation. In Equation (1) of the attached example, should the first column of matrix A be written as 0.8x1 + 0.2x2 , rather than x1 + 0.2x2 ? Thanks in advance for your inputs. example.pdf Edited October 31, 2016 by mikeraj Link to comment Share on other sites More sharing options...
Country Boy Posted November 1, 2016 Share Posted November 1, 2016 To write the first column of A, (.8, .2), as a linear combination of x1 and x2 we need to find numbers a and b such that (.8, .2)= a(.6, .4)+ b(1, -1)= (.6a+ b. .4a- b). That gives the two equation .6a+ b= .8 and .4a- b= .2. Adding the two equations eliminates b: (.6+ .4)a= a= .8+ .2= 1.0. With a= 1. .6a+ b= .6+ b= .8 so b= 0.2. It is 0.8x+ 0.2x2. Are you clear on what "x1" and "x2" are? Equation (1) writes (0.8, 0.2) as a linear combination of x1= (0.6, 0.4) and x2= (1, -1). That means we need to find numbers, a and b, such that a(0.6, 0.4)+ b(1, -1)= (0.6a+ b. 0.4a- b)= (0.8, 0.2). That gives the two equations 0.6a+ b= 0.8 and 0.4a- b= 0.2. Adding the two equations eliminates b: (0.6+ 0.4)a= a= 0.8+ 0.2= 1.0. Since a= 1, 0.6a+ b= 0.6+ b= 0.8 so b= 0.8- 0.6= 0.2. (0.8, 0.2)= 0.8(0.6, 0.4)+ 0.2(1, -1) is correct. Link to comment Share on other sites More sharing options...
mikeraj Posted November 1, 2016 Author Share Posted November 1, 2016 Hi HallsofIvy, I am clear now. Many thanks again! Link to comment Share on other sites More sharing options...
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