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

Every identity matrix is

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

The transpose of a row matrix is a ______

• Zero matrix A
• Diagonal matrix B
• Column matrix C
• Row matrix D

The square matrix A is skew Hermitian when (A)'=

• A A
• A' B
• -A C
• A D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

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

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

For a square matrix A, if A = At, then A is called

• Matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

• 0 A
• 1 B
• 2 C
• 3 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 diagonal matrix in which the diagonal elements are equal is called a

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

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None D

• 1 A
• -1 B
• 0 C
• I 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

System of linear equations is inconsistent if

• System has no solution A
• System has one solution B
• System has two solution C
• None of above D

• K/6 A
• 2K B
• 3K C
• 6K D

A matrix in which the number of rows is equal to the number of columns is called a

• Diagonal matrix A
• Rectangular matrix B
• Square matrix C
• Scalar matrix D

Matrices A = [aij] 2 x 3 and B =[bij] 3 x 2 are suitable for

• BA A
• A² B
• AB C
• B² D

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

• 1 A
• 0 B
• -1 C
• 2 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

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

For non-trival solution |A| is

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

• At A
• -A B
• A C
• A-1 D

• 
  A
• 
  B
• 
  C
• all are correct D

Matrices are represented by

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

If A is any matrix then its additive inverse is

• A A
• A^-1 B
• A^t C
• -A 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

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

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