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Mathematics Test - 3
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  • Question 1/10
    5 / -1

    Which of the following statements is/are true:

    I. A X = 0, always have a solution.

    II. It is not necessary that  A X = 0, will always have a solution.
  • Question 2/10
    5 / -1

    2x – 3y = 0 and 2x + αy = 0

    For what value of α the system has unique solution.

  • Question 3/10
    5 / -1

    Consider the below statements -

    (i) For a matrix system AX = B, there will be a unique solution only iff |A| ≠ 0.

    (ii) A system of equations will always be inconsistent if |A| = 0.

    (iii) If |A| = 0 and (adjA)B = 0, then the system will have infinite solutions.

    (iv) For consistency |A| will always be non-zero. 

    Then which of the following statements are true?

  • Question 4/10
    5 / -1
    For what value of α, the system of equation: x + y + z = 0, x – y + z = 0 and 2x + 3y + αz = 0 has infinitely many solutions.
  • Question 5/10
    5 / -1
    A non-singular matrix M = \(\begin{bmatrix} 3 & 6 & 9\\6 & 9 & 12\\9 & 12 & 18\end{bmatrix}\) is such that M-1 = \(\begin{bmatrix} -2/3 & 0 & 1/3\\0 & 1 & -2/3\\ 1/3& -2/3 & 1/3\end{bmatrix}\) . If the system of equations x + 2y + 3z = 5, 2x + 3y + 4z = 7, 3x + 4y + 6z = 11 has a unique solution then xyz = ?
  • Question 6/10
    5 / -1

    Consider the given system of simultaneous linear equations -

    x + ωy + ω2z = 0

    ωx + ω2y + z = 0

    ω2x + y + ωz = 0

    where ω is a complex cube root of unity. Then the system of equations has  

  • Question 7/10
    5 / -1
    If the system of equations px - 2y - pz = 0, 2x + py - pz = 0, -px + py + 2z = 0 has a non-trivial solution, then the sum of the possible values of p is
  • Question 8/10
    5 / -1
    For what values of k is the system of equations 2k2x + 3y - 1 = 0, 7x - 2y + 3 = 0, 6kx + y + 1 = 0 consistent?
  • Question 9/10
    5 / -1
    The given system of equations kx + 5y + 3z = 1, x + 3y + 2z = 3, x + 2y + z = 3 has no solution for -
  • Question 10/10
    5 / -1
    The system of equations kx + y + z = 1, x + ky + z = k and x + y + kz = k2 has no solution if k equals
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