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

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

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

• 
  A
• 
  B
• 
  C
• 
  D

• Hermitian matrix A
• Skew-hermitian matrix B
• Symmetric matrix C
• Identity matrix D

A square matrix A = [aij] is lower triangular matrix when:

• aij = 0 for all i < j A
• bij = 0 B
• cij = 0 C
• dij =0 D

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

• BA A
• A² B
• AB C
• B² D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

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

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 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

• 
  A
• 
  B
• 
  C
• 
  D

A matrix in which the number of rows is not equal to the number of columns is called a

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

• K/6 A
• 2K B
• 3K C
• 6K D

The transpose of a column matrix is a ______

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

• I3 A
• rI3 B
• r C
• none D

• 
  A
• 
  B
• 
  C
• 
  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

Every identity matrix is

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

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 D

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

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None D

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

• 
  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

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

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

The matrix A = [aij]1xn is a

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

• 
  A
• 
  B
• 
  C
• 
  D

• 5 A
• 
  B
• -5 C
• none D