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

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
• 
  B
• 
  C
• 
  D

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

The matrix A = [aij]mxn with m≠n is

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

A and B be two square matrices and if their inverse exist, the (AB)^-1=

• A^-1B^-1 A
• AB^-1 B
• A^-1B C
• B^-1A^-1 D

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

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

• I A
• |A| B
• |A| I C
• None of these D

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

A non-homogeneous linear system AX = B has no solution if

• |A| = 0 A
• |A|≠ 0 B
• Rank (a) = no of variables C
• Rank > no of variables D

The matrix A = [aij]1xn is a

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

• 
  A
• 
  B
• 
  C
• all are correct 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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 2 A
• 4 B
• 6 C
• 8 D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• At A
• -A B
• A C
• A-1 D

• A A
• -A B
• A^t C
• A^- D

• 
  A
• 
  B
• 
  C
• 
  D

If the trace of matrix A is 5, then the trace of the matrix 3A is

• 3/5 A
• 5/3 B
• 8 C
• 15 D

The transpose of a zero matrix is a ______

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

• 1 A
• 0 B
• -1 C
• 2 D

The transpose of a column matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  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