ECAT Mathematics Chapter 5 MCQ Test With Answer for Mathematics chapter 5 (Matrices and Determinants)

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

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

• 1 A
• 0 B
• 3 C
• -1 D

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

• A2 A
• A3 B
• A C
• None of above D

• 0 A
• 1 B
• 2 C
• 3 D

• 
  A
• 
  B
• 
  C
• 
  D

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

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

• 
  A
• 
  B
• 
  C
• all are correct D

The matrix A = [aij]1xn is a

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

• 
  A
• 
  B
• 
  C
• 
  D

• 6, -12, -18 A
• -6, 4, 9 B
• -6, -4, -9 C
• -6, 12, 18 D

• 1 A
• -1 B
• 0 C
• I D

• A A
• -A B
• A^t C
• A^- D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

Matrices are represented by

• Natural numbers A
• Real numbers B
• Small letters C
• Capital letters D

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

• 
  A
• 
  B
• 
  C
• 
  D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these 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 an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

• 
  A
• 
  B
• 
  C
• 
  D

Every identity matrix is

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

If the matrices A and B are conformable for multiplication then (AB)^t= ______

• AB A
• A^tB^t B
• B^tA^t C
• A^tB D

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

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

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  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

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