ECAT Pre General Science MCQ Test With Answer for Mathematics Chapter 5

A square matrix A for which A^t= A is called a

• Column matrix A
• Symmetric matrix B
• Skew-symmetric matrix C
• Row matrix D

A non-homogeneous linear system AX = B has no solution if

• |A| = 0 A
• |A|≠ 0 B
• Rank (a) = no of variables C
• Rank > no of variables D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

Matrices are represented by

• Natural numbers A
• Real numbers B
• Small letters C
• Capital letters D

Cofactor of an element a_ijis defined by

• (-1)^i+j|A| A
• (-1)^i+jM_ij B
• (-1)^i+jM^-1 C
• None of these D

For a square matrix A, if A = A^t, then A is called

• matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

A square matrix A = [aij] is upper triangular when

• cij = 0 A
• bij = 0 B
• aij = 0 for all i > j C
• dij = 0 D

Trival solution of homogeneous linear equation is

• (0, 0, 0) A
• (1, 2, 3) B
• (1, 3, 5) C
• a, b and c D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

If for the matrix A,A5 = 1,then A-1=

• A2 A
• A3 B
• A C
• None of above D

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries D

• I A
• |A| B
• |A| I C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

A diagonal matrix is always

• Identity A
• Triangular B
• Scalar C
• Non-singular D

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

• 1 A
• 0 B
• -1 C
• 2 D

• Null matrix A
• Triangular matrix B
• Unit matrix C
• Rectangular matrix D

• 
  A
• 
  B
• 
  C
• 
  D

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

• A2 A
• A5 B
• A3 C
• A7 D

A square matrix A = [aij] is lower triangular matrix when

• aij = 0 for all i<j A
• bij = 0 B
• cij = 0 C
• dij = 0 D

If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is

• Skew-symmetric A
• Symmetric B
• Null C
• Diagonal D

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

• A^- A
• A^t B
• -A C
• A D

• 
  A
• 
  B
• 
  C
• 
  D

A square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix D

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

• BA A
• A² B
• AB C
• B² D

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

• Diagonal matrix A
• Scalar matrix B
• Triangular matrix C
• Identity matrix D