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).

Related Further Mathematics A Level answers

All answers ▸

Use induction to prove that for all positive integers n, f(n)=2^(3n+1)+3x5^(2n+1) is divisible by 17.


How to solve a standard first order differential equation?


Write the Maclaurin’s series for f(x)=sin(3x)+e^x up to the third order


How do you solve, dy/dx=(x^2+y^2)/xy?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences