The discussion focuses on the calculation steps for determining the ratio X1:X2 after substituting the lower value of W^2 into equation 9.9 from "Riley, Hobson, Bence - Mathematical Methods for Physics and Engineering 2006 - pg 319". Participants clarify that matrices A and B, along with the scalar ω, are essential inputs for the computation. The resulting equation Cx=0 indicates that while there are two equations and two unknowns, the solutions are not independent due to the scalar multiplicity of the vector x, leading to infinite solutions expressed as a ratio.
PREREQUISITESStudents and professionals in physics and engineering, particularly those studying linear algebra and its applications in normal mode analysis. This discussion is beneficial for anyone looking to deepen their understanding of matrix equations and their solutions.
Thank you very much.Office_Shredder said:A and B are matrices you know, and ##\,omega## is a number that you know, so you can plug them all in and you get like like ##Cx=0## for some matrix ##C## that you know. You might at first guess that gives you two equations and two unknown (##x## is a vector of 2 dimensions, the 0 on the right side is also a vector of 2 dimensions so you get two equations) but if ##x## is a solution so is ##\alpha x## for any scalar ##\alpha##, which means the two equations are not independent, and there are infinite solutions. So all you can do is express one variable in terms of the other which is the same as computing their ratio