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

For any positive integer n

• ABn = Bn A ⇔ AB = BA A
• ABn = Bn A⇔ A,B are square matrices and AB = BA B
• ABn = BnA⇔ A + B C
• ABn = BnA ⇔ A and B are square matries D

• Singular A
• Non-singular B
• Adjoint C
• None of above D

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

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

Matrices are represented by

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

A diagonal matrix is always

• Identity A
• Triangular B
• Scalar C
• Non-singular D

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

• A² A
• A³ B
• A C
• None of above 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

• 
  A
• 
  B
• 
  C
• 
  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

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

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

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

• BA A
• A2 B
• AB C
• B2 D

If A is a non-singular matrix then adj A is

• Non-singular A
• Symmetric B
• Singular C
• Non defined D

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

• At A
• -A B
• A C
• A-1 D

• k3 A
• 0 B
• 3k C
• k6 D

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

• 16 A
• 256 B
• 64 C
• 1024 D

• 0 A
• 1 B
• -A C
• -1 D

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

Matrix multiplication is

• Commutative A
• Not commutative B
• Not associative C
• Not distributive 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

• x =0, y =4 A
• x = -1, y = 2 B
• x = 2, y = 3 C
• x = 3, y = 4 D

We also the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a, b and c D

The square matrix A is skew-symmetric when At=

• -B A
• -C B
• -A C
• -D D

• A A
• -A B
• A^t C
• A^- D

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

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