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Quiz

Year 3: Determinants and matrices

10 questions with solutions for year 3: 2×2 and 3×3 determinants, systems of three linear equations, matrix operations, matrix equations, Gaussian elimination – review problems.

Type the number or choose the right answer. When you finish, click Check answers and see the solutions.

1. | (1 − t)²/(1 + t²) 2t/(1 + t²) ; 2t/(1 + t²) −(1 + t)²/(1 + t²) | = ?

2. | (1 − t²)/(1 + t²) 2t/(1 + t²) ; −2t/(1 + t²) (1 − t²)/(1 + t²) | = ?

3. | 1 1 1 ; s+1 s+2 s+3 ; s+4 s+5 s+7 | = ?

4. Solve | 2 −1 x+2 ; 1 −2 1 ; 5 x −3 | < 0

5. For which a has the system 3x + 5y = 5, 2x − y = a, x + 2y = 1 a solution?

6. 2[x 0; 0 0] + 2[0 y; 0 0] = [0 0; z 0] + [0 0; 0 t]. Then:

7. A = [2 1; 0 3], B = [0 −1; −1 2]. (AB)ᵀ = ?

8. [1 2; 3 4] · X = [3 5; 5 9]. X = ?

9. Solve the system: 2x − 6y + 8z = 28, −2x + 4y − 10z = −26, 4x + 10y − 6z = −10

10. By Gaussian elimination: x − 2y + 3z = 10, 4x + y − 2z = 8, 2x + 3y + 5z = 5