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Questions › DSE › DSE 2012 › Q44
2 marksMathematics › Matrices, determinants and linear systems › Consistency, rank and solution spacesHardabout 4 min

DSE 2012 Question 44: Matrices, determinants and linear systems

Consider the system of equations αx+βy=0\alpha x+\beta y=0αx+βy=0 and μx+νy=0\mu x+\nu y=0μx+νy=0. α,β,μ\alpha,\beta,\muα,β,μ and ν\nuν are i.i.d random variable. Each of them takes value 1 and 0 with equal probability. Statement A: The probability that the system of equations has a unique solution is 38\frac{3}{8}83​. Statement B: The probability that the system of equations has at least one solution is 1.

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Consider the system of equations α x+β y=0 and μ x+ν y=0. α,β,μ and ν are i.i.d random variable. Each of them takes value 1 and 0 with equal probability. Statement A: The probability that the system of equations has a unique solution is 3/8. Statement B: The probability that the system of equations has at least one solution is 1. (A) Both the statements are correct (B) Both the statements are false (C) Statement A is correct but B is false (D) Statement B is correct but A is false

Also written as: Consider the system of equations alpha x+beta y=0 and mu x+nu y=0. alpha,beta,mu and nu are i.i.d random variable. Each of them takes value 1 and 0 with equal probability. Statement A: The probability that the system of equations has a unique solution is 3/8. Statement B: The probability that the system of equations has at least one solution is 1.

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 2012 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.