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

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

• A2 A
• A3 B
• A C
• None of above D

The transpose of a zero matrix is a ______

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

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

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

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

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

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

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

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

The transport of a square matrix is a

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all are correct D

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

A matrix in which the number of rows is not equal to the number of columns is called a

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

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

• A² A
• A³ B
• A C
• None of above 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

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

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

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

• BA A
• A2 B
• AB C
• B2 D

• At A
• -A B
• A C
• A-1 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' 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^- A
• A^t B
• -A C
• A 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

• 1 A
• 0 B
• 3 C
• -1 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

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

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

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

• -3 A
• -7 B
• 1 C
• 0 D

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 D