Show that the matrix A is non-singular for all real values of a

Given: A = [a -5; 2 a+4]. 1) First find the determinant of A using the known formula => det A = a2+ 4a + 10. A singular matrix is one in which it's determinant equals zero (the determinant of a matrix is a number that captures information about the characteristics of the matrix). The roots of the quadratic are complex, so the graph never equals zero/ no real roots. Therefore it must be a non-singular matrix.

Related Further Mathematics A Level answers

All answers ▸

Further Maths: How do you find the inverse of a 2 x 2 matrix?


Prove ∑r^3 = 1/4 n^2(n+1)^2


What is the modulus of 3+4i?


Prove by induction the sum of n consecutive positive integers is of the form n(n+1)/2.


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