FP3- Find the eigenvalues and the eigenvector for the negative eigenvalue, from this 2x2 matrix of columns (2,1) and (3,0)

Let the 2x2 matrix= A. Using the characteristic equation for A (det(A-λI)=0), find the determinant of the matrix (2-λ,1) and (3,-λ). This results in the quadratic λ^2-2λ-3 so λ=3,-1. From the definition of the eigenvector,v, Av=λv. Let v be the column vector (x,y), and for λ=-1 we get the simultaneous equations 2x+3y=x and x=-y, which results in the eigenvector (1,-1).

BM
Answered by Ben M. Further Mathematics tutor

2635 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution to f''(x)+ 3f'(x)+ 2f(x)=0


Integrate x^2sin(x) between -pi and pi


I don't know what I am doing when I solve differential equations using the integrating factor and why does this give us the solutions it does?


How do you plot a complex number in an Argand diagram?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences