Given that k is a real number and that A = ((1+k k)(k 1-k)) find the exact values of k for which A is a singular matrix.

okay so A is a 2x2 matrix.for it to be singular its determinate has to equal 0.a 2x2 matrix's determinate is equal to m1,1m2,2 - m1,2m2,1for this example:det(A) = (1+k)(1-k) - (k)(k) = 0multiplying out the brackets(1+k)(1-k) becomes 1-k+k-k2 = 1-k2(k)(k) becomes k2so det(A)= 1-k2-k2 = 1-2k2 = 0solving for k1=2k21/2 = k2so k = +/-SQRT(1/2)

KY
Answered by Kieran Y. Further Mathematics tutor

3307 Views

See similar Further Mathematics A Level tutors

Related Further Mathematics A Level answers

All answers ▸

By forming and solving a suitable quadratic equation, find the solutions of the equation: 3cos(2A)-5cos(A)+2=0


Express (X²-16)/(X-1)(X+3) in partial fractions


Find the modulus-argument form of the complex number z=(5√ 3 - 5i)


Prove De Moivre's by induction for the positive integers


We're here to help

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

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences