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Matrices Test - 6
Result
Matrices Test - 6

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  • Question 1/10
    1 / -0.25

    Solutions

    A square matrix A for which An = 0 , where n is a positive integer, is called a Nilpotent matrix.

  • Question 2/10
    1 / -0.25

    Solutions






  • Question 3/10
    1 / -0.25

    If A any square matrix then which of the following is not symmetric ?

    Solutions

    For every square matrix (A –A ’) is always skew –symmetric.

  • Question 4/10
    1 / -0.25

    Let a, b, c, d, u, v be integers. If the system of equations, a x + b y = u, c x + dy = v, has a unique solution in integers, then

    Solutions


    ax + by = u , cx +dy = v , 

    since the solution is unique in integers.



  • Question 5/10
    1 / -0.25

    The system of equations, x + y + z = 1, 3 x + 6 y + z = 8, αx + 2 y + 3z = 1 has a unique solution for

    Solutions

    The given system of equations has unique solution , if  


    ⇒1(18 −2)−1(9 −α) ⇒13 −5 α≠0 ⇒α≠13/5  + 1(6 −6 α) ≠0
    Therefore , unique solution exists for all integral values of  α.

  • Question 6/10
    1 / -0.25

    If A and B are symmetric matrices of the same order, then

    Solutions

    If A and B are symmetric matrices of the same order, then , AB + BA is always a symmetric matrix.

  • Question 7/10
    1 / -0.25

    If  A = [aij ]2 ×2 where  aij = i  + j, then A is equal to

    Solutions

    If A = [aij ]2x2  where aij  = i + j, then, 

  • Question 8/10
    1 / -0.25

    Each diagonal element of a skew-symmetric matrix is

    Solutions

    The diagonal elements of a skew-symmetric is zero.

  • Question 9/10
    1 / -0.25

    The system of equations, x + y + z = 6, x + 2 y + 3 z = 14, x + 3 y + 5z = 20 has

    Solutions

    The given system of equations does not has a solution if : 


     

    0 ⇒1(10 -9) - 1(5-3) + 1(3-2)

    = 0 ⇒1-2 + 1 = 0

  • Question 10/10
    1 / -0.25

    The matrix of the transformation ‘reflection in the line x + y = 0 ‘is

    Solutions

    Let x 'and y 'be the reflection of x and y, therefore :



    Hence, reflection is on the line - x-y = 0 ⇒x + y = 0

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