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.

Answered by Further Mathematics tutor

6956 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

How far is the point (7,4,1) from the line that passes through the points (6,4,1) and (6,3,-1)?


Find the solution the the differential equation d^2y/dx^2 + (3/2)dy/dx + y = 22e^(-4x)


A particle is projected from the top of a cliff, 20m above the sea level at an angle of 30 degrees above the horizontal at 20m/s. At what vertical speed does it hit the water?


How do I know which substitution to use if I am integrating by substitution?


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