ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the 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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• Singular A
• Non-singular B
• Adjoint C
• None of above D

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 D

For non-trival solution |A| is

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

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

• A^- A
• A^t B
• -A C
• A D

• 
  A
• 
  B
• 
  C
• 
  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

• 0 A
• 1 B
• 2 C
• 3 D

For trival solution |A| is

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

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  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

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

• 3K A
• K2 B
• K3 C
• K D

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

(ABC)' =

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

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these D

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix D

• 
  A
• 
  B
• 
  C
• 
  D

A matrix with a single row is called a

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

A diagonal matrix is always

• Identity A
• Triangular B
• Scalar C
• Non-singular D

The transport of a rectangular matrix is a

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

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D