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

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• A2 A
• A3 B
• A C
• None of above D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

A diagonal matrix is always

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

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

• 0 A
• 1 B
• -A C
• -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

Matrix multiplication is

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

• 3, -3, 11 A
• 3, 3, 11 B
• -3, 3, -11 C
• -3, -3, 11 D

The transpose of a column matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• a²b²c² A
• 4a²b²c² B
• 4abc C
• None D

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 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

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

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

• 0 A
• 1 B
• 2 C
• 3 D

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 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

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

• K/6 A
• 2K B
• 3K C
• 6K D

• 
  A
• 
  B
• 16 C
• None of these D

• Singular A
• Non-singular B
• Adjoint 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

Trival solution of homogeneous linear equation is

• (0, 0, 0) A
• (1, 2, 3) B
• (1, 3, 5) C
• a.b and c D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

The matrix A = [aij]1xn is a

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