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

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

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

• x =0, y =4 A
• x = -1, y = 2 B
• x = 2, y = 3 C
• x = 3, y = 4 D

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) D

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

• k3 A
• 0 B
• 3k C
• k6 D

• 9/4 A
• 4/9 B
• 1 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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• A A
• A' B
• -A 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

If there are m rows and n columns in a matrix then its order is

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

• 6, -12, -18 A
• -6, 4, 9 B
• -6, -4, -9 C
• -6, 12, 18 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

• A A
• -A B
• A^t C
• A^- D

The matrix A = [aij]1xn is a

• Vector A
• Rectangular matrix B
• Column vector C
• Square matrix D

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all are correct D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

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

• 
  A
• 
  B
• 
  C
• 
  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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D 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

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