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

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

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 
  A
• 
  B
• 
  C
• all are correct 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

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' 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 square matrix A = [aij] is upper triangular when

• cij = 0 A
• bij = 0 B
• aij = 0 for all i > j C
• dij = 0 D

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

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

• A2 A
• A3 B
• A C
• None of above D

• 0 A
• abc B
• 1/abc C
• None of these D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

• Null matrix A
• Triangular matrix B
• Unit matrix C
• Rectangular matrix D

The matrix A = [aij]1xn is a

• Vector A
• Rectangular matrix B
• Column vector C
• Square matrix D

• -a -b -c A
• 1 B
• 0 C
• -1 D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

• 
  A
• 
  B
• 
  C
• 
  D

• 1 A
• 0 B
• -1 C
• 2 D

• 
  A
• 
  B
• 
  C
• 
  D

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

A square matrix A = [aij] is lower triangular matrix when

• aij = 0 for all i<j A
• bij = 0 B
• cij = 0 C
• dij = 0 D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all D

• 16 A
• 256 B
• 64 C
• 1024 D

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

• k3 A
• 0 B
• 3k C
• k6 D

A diagonal matrix in which the diagonal elements are equal is called a

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

If A and B are two matrices such that AB = B and BA = A then A2 + B2 =

• 2 AB A
• 2 BA B
• A + B C
• AB D

If A is a non singular matrix then A^-1= ______

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• all are correct D