Find the eigenvalues and corresponding eigenvectors of the following matrix: A = [[6, -3], [4, -1]]. Hence represent the matrix in diagonal form.

The first eigenvalue is 3, whose corresponding eigenvector is (1, 1), and the second eigenvalue is 2, whose corresponding eigenvector is (3, 4). In diagonal form, A = PDP^-1, where P = [[1, 3], [1, 4]] and D = [[3, 0], [0, 2]].

MU
Answered by Michael U. Further Mathematics tutor

3304 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

Given that p≥ -1 , prove by induction that, for all integers n≥1 , (1+p)^k ≥ 1+k*p.


A line has Cartesian equations x−p = (y+2)/q = 3−z and a plane has equation r ∙ [1,−1,−2] = −3. In the case where the angle θ between the line and the plane satisfies sin⁡θ=1/√6 and the line intersects the plane at z = 0. Find p and q.


If 0<x<1, find the following sum: S = 1+2*x + 3*x^2 + 4*x^3 + ...


What are the conditions required for the poisson distribution?


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:

© 2026 by IXL Learning