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Questions › DSE › DSE 2009 › Q23
2 marksMathematics › Matrices, determinants and linear systems › Consistency, rank and solution spacesHardabout 3 min

DSE 2009 Question 23: Matrices, determinants and linear systems

Consider the system in unknowns xxx and yyy: ax+y=a2ax+y=a^{2}ax+y=a2 and x+ay=1x+ay=1x+ay=1. Sets of all values of aaa for which this system has (i) no solution, (ii) multiple solutions and (iii) a unique solution are respectively

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Consider the system in unknowns x and y: ax+y=a² and x+ay=1. Sets of all values of a for which this system has (i) no solution, (ii) multiple solutions and (iii) a unique solution are respectively (A) (i) a<1 (ii) a>1 (iii) a=1 (B) (i) a=-1 (ii) a=1 (iii) a>1 (C) (i) a=-1 (ii) a=1 (iii) all other values of a (D) (i) a=-1 (ii) a=1 (iii) -1<a<+1

Also written as: Consider the system in unknowns x and y: ax+y=a^2 and x+ay=1. Sets of all values of a for which this system has (i) no solution, (ii) multiple solutions and (iii) a unique solution are respectively

Matrices, determinants and linear systems has come up 102 times in 7 exams since 2006.

What this question tests

This question is on Consistency, rank and solution spaces, part of Matrices, determinants and linear systems in Mathematics.

Whether a system has no solution, one or many, and the shape of its solution set.

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Question from the DSE 2009 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.