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

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

• 
  A
• 
  B
• 
  C
• 
  D

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

For trival solution |A| is

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

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

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

• 1 A
• -1 B
• 0 C
• I D

• 0 A
• Independent of a B
• Independent of b C
• Independent of c D

Minor of an element a_ijis denoted by

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

The number of non zero rows in echelon form of a matrix is called

• Order of matrix A
• Rank of matrix B
• Row operation C
• None of these D

For trival solution |A| is

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

• 5 A
• 
  B
• -5 C
• none D

• Hermitian matrix A
• Skew-hermitian matrix B
• Symmetric matrix C
• Identity matrix D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  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

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

• -a -b -c A
• 1 B
• 0 C
• -1 D

• 
  A
• 
  B
• 
  C
• 
  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
• 
  B
• 
  C
• 
  D

Matrices are represented by

• Natural numbers A
• Real numbers B
• Small letters C
• Capital letters 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