ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

Which of the following is skew symmetric matrix

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 2 C
• 3 D

• 
  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 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

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

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

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

Two matrices A and B are conformable for the product AB if

• Both A and B are square A
• Both A and B are symmetric B
• Number of rows of A = number of columns of B C
• Number of columns of A = number of rows of B D

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

The transpose of a row matrix is a ______

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

• 1 A
• 0 B
• -1 C
• 2 D

• 
  A
• 
  B
• 
  C
• 
  D

A diagonal matrix in which the diagonal elements are equal is called a

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

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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' 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

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| 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

Matrix multiplication is

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

• A A
• -A B
• A^t C
• A^- D

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

• A² A
• A³ B
• A C
• None of above 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

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