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NDA - Matrices Test 1190
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NDA - Matrices Test 1190
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  • Question 1/5
    1 / -0.33
    , . If AB = C, then what is A2 equal to?
    Solutions

    Given that ,


    And AB = C,


    ⇒


    As number of columns of pre matrix is equal to the number of rows of post matrix so we can multiply A and B.


    ⇒


    If two matrix are equal then their corresponding elements are also equal.


    ⇒


    ……………..(1)


    ⇒


    ………….(2)


    Multiply equation (1) by 2 and subtract from equation (2)


    ⇒


    ⇒


    ⇒ x = 2


    Put value of x in equation (1)


    ⇒


    ⇒


    Hence =


    ⇒

  • Question 2/5
    1 / -0.33
    If the maximum number of distinct entries in lower triangular matrix of order n is 16 then find the value of ‘n’.
    Solutions

    we know that square matrix is called lower triangular matrix if all its entries above the main diagonal are zero.

    Maximum number of distinct entries in lower triangular matrix of order n =

    ⇒

    ⇒

    ⇒

    ⇒

    ⇒

    ⇒

    ⇒

    But order of a matrix can never be negative. So n = 5.

  • Question 3/5
    1 / -0.33
    The matrix A has x rows and  columns. The matrix B has y rows and  columns. Both AB and BA exist. What are the values of x and y respectively?
    Solutions

    Let A =

    And B =

    If AB exist then number of columns of A is equal to number of rows in B

    ⇒

    If BA exist then number of columns of B is equal to number of rows in A

    ⇒ ……………………(2)

    Put the value of x from (2) into (1)

    ⇒

    ⇒

    Put the value of y into (1)

    ⇒

    ⇒

  • Question 4/5
    1 / -0.33
     then  is
    Solutions

     Let A =

    Then

    We know that

    So

    We will first evaluate

    Let B =

    The inverse of B is given by

    Now Cofactor of a11 =

    Cofactor of a12 =

    Cofactor of a21 =

    Cofactor of a22 =

    =

    ⇒

    Two matrices are equal if their corresponding elements are equal

    Hence

  • Question 5/5
    1 / -0.33
    If  then which one of the following is correct?
    Solutions

    =

    =>

    =

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