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

If A = |aij| 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 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

• -a -b -c A
• 1 B
• 0 C
• -1 D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

The transpose of a row matrix is a ______

• Zero matrix A
• Diagonal matrix B
• Column 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 square matrix A for which A^t= -A is called a

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

• -3 A
• -7 B
• 1 C
• 0 D

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| C
• None of these D

• 5 A
• 
  B
• -5 C
• none D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

• 
  A
• 
  B
• 16 C
• None of these D

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

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

A matrix in which the number of rows is equal to the number of columns is called a

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

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

The matrix A = [aij]mxn with m≠n is

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

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

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

• Square matrix A
• Row matrix B
• Symmetric matrix C
• Null matrix D

• 
  A
• 
  B
• 
  C
• 
  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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

The square matrix A is skew Hermitian when (A)'=

• A A
• A' B
• -A C
• A D

• 9/4 A
• 4/9 B
• 1 C
• None of these D

• 16 A
• 256 B
• 64 C
• 1024 D

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 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