mikeraj 0 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 0.8x_{1} + 0.2x_{2} , rather than x_{1} + 0.2x_{2} ? Thanks in advance for your inputs. example.pdf Edited October 31, 2016 by mikeraj Share this post Link to post Share on other sites

HallsofIvy 50 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. Share this post Link to post Share on other sites

mikeraj 0 Posted November 1, 2016 Hi HallsofIvy, I am clear now. Many thanks again! Share this post Link to post Share on other sites