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Questions › UoH › UoH 2020 › Q38
1 mark, −0.33Mathematics › Matrices, determinants and linear systems › Consistency, rank and solution spacesModerateabout 1 min

UoH 2020 Question 38: Matrices, determinants and linear systems

For the next TWO (37 and 38) questions consider the following system of equations:

2x1−x2+3x3=5(1);−x1+2x2−2x3=0(2)2x_1 - x_2 + 3x_3 = 5 \quad (1); \qquad -x_1 + 2x_2 - 2x_3 = 0 \quad (2)2x1​−x2​+3x3​=5(1);−x1​+2x2​−2x3​=0(2)

How many total number of solutions does this system of equations have?

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Plain-text version

For the next TWO (37 and 38) questions consider the following system of equations: 2x₁ - x₂ + 3x₃ = 5 (1); -x₁ + 2x₂ - 2x₃ = 0 (2) How many total number of solutions does this system of equations have? (A) No solution; (B) One unique solution; (C) Three solutions; (D) Infinitely many solutions

Also written as: For the next TWO (37 and 38) questions consider the following system of equations: 2x_1 - x_2 + 3x_3 = 5 (1); -x_1 + 2x_2 - 2x_3 = 0 (2) How many total number of solutions does this system of equations have?

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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Question from the UoH 2020 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.