ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 5 (Matrices and Determinants)

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 1 A
• -1 B
• 0 C
• I D

• a = -1/2, b = -1 A
• a = 1, b = 2 B
• a = 2, b = 3 C
• None of above D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

• 
  A
• 
  B
• 
  C
• 
  D

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 D

A = [3] is a/an

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

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

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

• 1 A
• 0 B
• -1 C
• 2 D

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

(ABC)' =

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

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

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 additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

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

• 5 A
• 15 B
• 10 C
• 20 D

• 
  A
• 
  B
• 
  C
• 
  D

If the matrices A and B are conformable for multiplication then (AB)^t= ______

• AB A
• A^tB^t B
• B^tA^t C
• A^tB D

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

• 
  A
• 
  B
• 
  C
• 
  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