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

For trival solution |A| is

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

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

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

• 
  A
• 
  B
• 
  C
• 
  D

• A^- A
• A^t B
• -A C
• A D

• 5 A
• 
  B
• -5 C
• none 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

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

For non-trival solution |A| is

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

For a square matrix A, if A = A^t, then A is called

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

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

• A A
• -A B
• A^t C
• A^- D

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

• 
  A
• 
  B
• 
  C
• 
  D

We solve the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a,b and c D

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

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 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

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

A square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix 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

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

System of linear equation is inconsistent if

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

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 
  A
• 
  B
• 
  C
• 
  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

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