Engineering Maths - Linear Algebra


Linear Algebra  GATE Syllabus

Matrices, determinants, system of linear equations, eigenvalues and eigenvectors, LU decomposition.


 

1. Rank of the matrix A =

0 0 0 0
4 2 3 0
1 0 0 0
4 0 3 0

  • 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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  • These Linear Algebra multiple choice questions answers can be used by any Engineering student to gain good credit score.
  • Linear Algebra Objective Type questions answers can also be used by FY B. Sc. Students to prepare for their exams.
  • B. Sc. Maths and M.Sc. Maths students can also use these Linear Algebra Practice Questions.
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