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

A matrix with a single row is called a

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

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  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

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

• I A
• 14 I B
• 0 C
• None of these D

• 3 x 1 A
• 1 x 3 B
• 3 x 3 C
• 1 x 1 D

• 
  A
• 
  B
• 
  C
• 
  D

If A = [a_ij] is (m x n) matrix, then transpose of A is of the order

• m x m A
• m x n B
• n x n C
• n x m 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

• 5 A
• 
  B
• -5 C
• none D

For trival solution |A| is

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

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

• k3 A
• 0 B
• 3k C
• k6 D

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

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

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

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

A diagonal matrix is always

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

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

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

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

• 1 A
• 0 B
• -1 C
• 2 D

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

• BA A
• A2 B
• AB C
• B2 D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

• A2 A
• A3 B
• A C
• None of above D

Every identity matrix is

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

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