Prime DSE Series - Mathematics Mock Exam Papers (Extended Part) Module 2 Set 3

HKDSE-MATH-EP(M2)(Set 3) − 12 12 © United Prime Educational Publishing (HK) Ltd. Answers written in the margins will not be marked. Answers written in the margins will not be marked. Answers written in the margins will not be marked. 8. Consider the system of linear equations in real variables x , y , z 6 (3 7) 4 3 ( ) : ( 1) 2 3 ( 3) (2 7) 3 x a y z E x a y z b x a y a z b + + + =   + + − = −   + + + + = −  , where , a b ∈ R . (a) Assume that ( E ) has a unique solution. Find the range of values of a . (b) Assume that 3 a ≠ − and ( E ) is inconsistent. Find the range of values of b . (c) Assume that 3 a = − . If ( E ) has infinitely many solutions, solve ( E ) . (8 marks) Sample © United Prime Educational Publishing (HK) Limited All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publisher.