4.03n-t Matrix inverses, simultaneous equations and planes meeting Quiz: OCR Further Maths, Unit 1

The 20 questions

1. What term describes a square matrix that does not have an inverse?

   • Non-singular
   • Symmetric
   • Identity
   • Singular

2. How do three planes intersect when their system of linear equations has a unique solution?

   • As a prism
   • Parallel planes
   • At a point
   • In a line

3. What shape do three inconsistent planes form if no two of the planes are parallel?

   • Sheaf
   • Single plane
   • Triangular prism
   • Single point

4. What name is given to the transpose of the matrix of cofactors of matrix A?

   • Adjugate matrix
   • Trace matrix
   • Inverse matrix
   • Identity matrix

5. If a square matrix A has a determinant of 4, what is det(A^-1)?

   • 1/4
   • 4
   • 1/16
   • -4

6. How do three distinct planes intersect if their corresponding system of equations has infinitely many solutions?

   • They never meet
   • At a point
   • As a prism
   • In a line

7. What matrix is produced when an invertible matrix A is multiplied by its inverse?

   • Zero matrix
   • Transpose matrix
   • Identity matrix
   • Singular matrix

8. For two invertible square matrices A and B, which expression is equal to (AB)^-1?

   • B A^-1
   • B^-1 A^-1
   • A B^-1
   • A^-1 B^-1

9. If A is a 3x3 matrix with det(A) = 5, what is det(2A)?

   • 10
   • 30
   • 40
   • 20

10. Which condition guarantees that a system of three linear equations in three variables has a unique solution?

    • det(A) < 0
    • det(A) != 0
    • det(A) = 0
    • det(A) = 1

11. What is the inverse of the diagonal 2x2 matrix with entries 2 and 4?

    • diag(1/2, 1/4)
    • diag(4, 2)
    • diag(-2, -4)
    • diag(2, 4)

12. How many solutions exist for a system representing three distinct parallel planes?

    • Three
    • One
    • Infinitely many
    • Zero

13. What term describes a system of linear equations that has no solutions at all?

    • Inconsistent
    • Dependent
    • Consistent
    • Singular

14. What is the formula for the determinant of a 2x2 matrix with rows (a,b) and (c,d)?

    • ac - bd
    • ab - cd
    • ad + bc
    • ad - bc

15. If A and B are square matrices with det(AB) = 12 and det(A) = 3, what is det(B)?

    • 36
    • 4
    • 15
    • 9

16. What specific term describes three planes that intersect along a single common line?

    • A sheaf
    • A prism
    • A star
    • A stack

17. If det(A) = 0 for a consistent system of three planes, how many solutions exist?

    • Exactly one
    • Exactly three
    • Infinitely many
    • Zero

18. What is the cofactor C_12 of the 2x2 matrix with top row (1, 2) and bottom row (3, 4)?

    • -3
    • 4
    • 3
    • -4

19. If a square matrix A is equal to its own inverse, what is A^2?

    • Matrix A
    • Scalar matrix
    • Identity matrix
    • Zero matrix

20. Why does the formula for the inverse of matrix A fail when det(A) = 0?

    • Zero identity
    • Negative determinant
    • Division by zero
    • Non-square matrix

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