ECAT Mathematics Chapter 5 Matrices and Detarminants

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

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

• I A
• 14 I B
• 0 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

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' 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

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

The transport of a square matrix is a

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

• 16 A
• 256 B
• 64 C
• 1024 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

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

• 
  A
• 
  B
• 
  C
• all are correct D

• 
  A
• 
  B
• 
  C
• 
  D

Matrices are represented by

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

• 
  A
• 
  B
• 
  C
• 
  D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

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

• 
  A
• 
  B
• 16 C
• None of these 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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 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 non-trival solution |A| is

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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