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

The order of the matrix A is 3 x 2 and that of B is 2 x 3. The order of the matrix BA is

• 3 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

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

• a = -1/2, b = -1 A
• a = 1, b = 2 B
• a = 2, b = 3 C
• None of above D

• 3K A
• K2 B
• K3 C
• K D

• 
  A
• 
  B
• 
  C
• 
  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

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

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

• 1 A
• -1 B
• 0 C
• I D

• 0 A
• 1 B
• 2 C
• 4 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

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 singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

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

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

• 0 A
• 1 B
• -A C
• -1 D

• 
  A
• 
  B
• 16 C
• None of these D

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

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

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

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

• A² A
• A³ B
• A C
• None of above D

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 D

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

The transpose of a row matrix is a ______

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

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) D

• I3 A
• rI3 B
• r C
• none D

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

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D