Engineering Maths - Linear Algebra

1. Rank of the matrix A =

 
0000
4230
1000
4030
 

  • Option : D
  • Explanation : Determinant A = 0

    4 2 3
    1 0 0
    4 0 3

    Hence rank of A=3

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2. A set of linear equations is represented by the matrix equation Ax = b. The necessary condition for the existence of a solution for this system is

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3. The system of linear equations                                                           (4d - 1)x +y + z = 0                                                                                 - y + z = 0                                                                                             (4d - 1) z = 0                                                                                             has a non-trivial solution, if d equals

  • Option : B
  • Explanation : The system of homogeneous linear equations has a non-trivial solution if

     
    4d-1 1 1
    0 -1 1
    0 0 4d-1
     
    = 0

    => -(4d-1)2 = 0

    => d = 1/4

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4. The rank of a 3 x 3 matrix C (= AB), found by multiplying a non-zero column matrix A of size 3 x 1 and a non-zero row matrix B of size 1 x 3, is

  • Option : B
  • Explanation :
    Let A =
     
    a1
    b1
    c1
     
    ; B =
     
    a2 b2 c2
     
    ;

    C =
     
    a1a2   a1b2   a1c2
    b1a2   b1b2   b1c2
    c1a1   c1b2   c1c2
     
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5. If A and B are square matrices of size n x n, then which of the following statement is not true?

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