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

In order of A is m x n and order of B is n x p then order of AB is

• m x m A
• n x n B
• m x p C
• p x m D

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

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

• A2 A
• A3 B
• A C
• None of above 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
• 
  B
• 
  C
• 
  D

(ABC)' =

• CBA' A
• CBA B
• C' B' A' C
• None of these D

• I3 A
• rI3 B
• r C
• none D

• 0 A
• 1 B
• -A C
• -1 D

A matrix with a single column is called

• Column matrix A
• Row matrix B
• Identity matrix C
• Null matrix D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 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

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

The number of non zero rows in echelon form of a matrix is called

• Order of matrix A
• Rank of matrix B
• Row operation C
• None of these D

An equation of the form ax + by = k is homogeneous linear equation when

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  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

• A^- A
• A^t B
• -A C
• A D

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

If the matrices A and B have the order 1 x 10 and 10 x 1 then order of AB is

• 1 x 1 A
• 1 x 10 B
• 10 x 10 C
• 10 x 1 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

• k3 A
• 0 B
• 3k C
• k6 D

• 
  A
• 
  B
• 
  C
• 
  D

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