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

2715 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Find the general solution to: d^(2)x/dt^(2) + 7 dx/dt + 12x = 2e^(-t)


Use De Moivre's Theorem to show that if z = cos(q)+isin(q), then (z^n)+(z^-n) = 2cos(nq) and (z^n)-(z^-n)=2isin(nq).


Find the general solution for the determinant of a 3x3 martix. When does the inverse of this matrix not exist?


Using mathematical induction, prove that n^3+2n is divisible by 3 for all integers n


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning