1.16 Systems of linear equations

1.16 Systems of linear equations Quiz

IB Maths: Analysis and Approaches HL: Quiz

Studying this course? Keep your progress in one place.

Pick an answer for each. Quizzes never use energy.

5 questions, one answer each

Each answer is checked as you go, with why.

See all 5 questions

1. Row reduction of a system gives the final row $0x + 0y + 0z = 4$ . The system has
- A. no solution
- B. a unique solution
- C. infinitely many solutions
- D. exactly two solutions
2. Which triple solves $x + y + z = 4$ , $x - y = 1$ , $2z = 2$ ?
- A. $(2, 1, 1)$
- B. $(1, 2, 1)$
- C. $(2, 1, 2)$
- D. $(3, 2, 1)$
3. A general solution is $x = 2 + \lambda$ , $y = 1 - 3\lambda$ , $z = \lambda$ . Which point is a solution?
- A. $(3, -2, 1)$
- B. $(3, 4, 1)$
- C. $(2, 1, 1)$
- D. $(4, -5, 1)$
4. For $x + y + z = 1$ , $x + 2y + z = 3$ , $2x + 3y + 2z = k$ , reduction gives $0 = k - 4$ . Which is true?
- A. Infinitely many solutions when $k = 4$
- B. A unique solution when $k = 4$
- C. No solution when $k = 4$
- D. A unique solution for all $k$
5. How many solutions can a system of three linear equations in three unknowns NOT have?
- A. Exactly two
- B. None
- C. Exactly one
- D. Infinitely many