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Questions › DSE › DSE 2021 › Q9
4 marks, −1Mathematics › Matrices, determinants and linear systems › Consistency, rank and solution spacesEasyabout 2 min

DSE 2021 Question 9: Matrices, determinants and linear systems

Consider the following system of equations in the unknowns x1,x2,x3x_1, x_2, x_3x1​,x2​,x3​, with λ\lambdaλ a real parameter: x1+2x2−2x3=0x_1 + 2x_2 - 2x_3 = 0x1​+2x2​−2x3​=0,   2x1−x2+λx3=0\; 2x_1 - x_2 + \lambda x_3 = 02x1​−x2​+λx3​=0,   3x1+x2−x3=0\; 3x_1 + x_2 - x_3 = 03x1​+x2​−x3​=0. Under which of the following conditions does this system have nonzero solutions?

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Consider the following system of equations in the unknowns x₁, x₂, x₃, with λ a real parameter: x₁ + 2x₂ - 2x₃ = 0, 2x₁ - x₂ + λ x₃ = 0, 3x₁ + x₂ - x₃ = 0. Under which of the following conditions does this system have nonzero solutions? (A) For both positive and negative values of λ (B) For more than one positive value of λ (C) For λ = 1 (D) For more than one negative value of λ

Also written as: Consider the following system of equations in the unknowns x_1, x_2, x_3, with lambda a real parameter: x_1 + 2x_2 - 2x_3 = 0, 2x_1 - x_2 + lambda x_3 = 0, 3x_1 + x_2 - x_3 = 0. Under which of the following conditions does this system have nonzero solutions?

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.

TestStop has 20 past-paper questions on this subtopic; the nearest in year are below.

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