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

If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is

• Skew-symmetric A
• Symmetric B
• Null C
• Diagonal D

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these 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

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

• k3 A
• 0 B
• 3k C
• k6 D

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

The transpose of a row matrix is a ______

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

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

The matrix A = [aij]mxn with m≠n is

• Rectangular A
• Symmetric B
• Square C
• None D

• -a -b -c A
• 1 B
• 0 C
• -1 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

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

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

If A = |aij| 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

A matrix with a single row is called a

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• A A
• -A B
• A^t C
• A^- D

• 
  A
• 
  B
• 
  C
• 
  D

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

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

If A = [aij]mxpand B =[aij]pxnthen order of BA is

• m x n A
• p x n B
• n x m C
• None of these 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

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D