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

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

The transpose of a row matrix is a ______

• Zero matrix A
• Diagonal matrix B
• Column matrix C
• Row matrix D

If order of A is m x n, then order of A^tis

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

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

• 
  A
• 
  B
• 
  C
• 
  D

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix 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

• 1 A
• 0 B
• -1 C
• 2 D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

A diagonal matrix in which the diagonal elements are equal is called a

• Null matrix A
• Identity matrix B
• Scalar matrix C
• Row 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

A diagonal matrix is always

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

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

• 2 x 2 A
• 2 x 3 B
• 3 x 2 C
• 3 x 3 D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

We solve the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a,b and c D

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 D

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None D

• 
  A
• 
  B
• 
  C
• 
  D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

A and B be two square matrices and if their inverse exist the (AB)-1 =

• A-1 B-1 A
• AB-1 B
• A-1B C
• B-1A-1 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

A matrix with a single column is called

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

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

System of linear equation is inconsistent if

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 D

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A D