ECAT Pre General Science Mathematics Chapter 5 Matrics and Determinants Online Test

• 1 A
• 0 B
• -1 C
• 2 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

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

Cofactor of an element aij denoted by Aij is

• (-2)i+j A
• Mij B
• (-1)i+j Mij C
• None of above D

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

A = [3] is a/an

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

If A is a non-singular matrix then adj A is

• Non-singular A
• Symmetric B
• Singular C
• Non defined D

An equation of the form ax + by = k is homogeneous linear equation when:

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 3 x 1 A
• 1 x 3 B
• 3 x 3 C
• 1 x 1 D

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

• m x m A
• m x n B
• n x n C
• n x m 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

A matrix with a single column is called

• Column matrix A
• Row matrix B
• Identity matrix C
• Null matrix D

• 0 A
• Independent of a B
• Independent of b C
• Independent of c D

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

• A² A
• A³ B
• A C
• None of above D

• A A
• -A B
• A^t C
• A^- D

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

• 2 AB A
• 2 BA B
• A + B C
• AB D

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

(ABC)' =

• CBA' A
• CBA B
• C' B' A' C
• None of these D

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B D

• 
  A
• 
  B
• 
  C
• all are correct D

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

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

• Scalar matrix A
• Identity matrix B
• Null matrix C
• Symmetric matrix D

System of linear equations is inconsistent if

• System has no solution A
• System has one solution B
• System has two solution C
• None of above D

• 
  A
• 
  B
• 
  C
• 
  D

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