ECAT (Pre-Eng) Mathematics Chapter 5 Matrices and Determinants

If A and B are skew-symmetric then (AB)t is

• At Bt A
• AB B
• -AB C
• BA D

• Orthogonal A
• Involutary B
• Idempotent C
• Nilpotent D

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

A square matrix A = [aij] is lower triangular matrix when:

• aij = 0 for all i < j A
• bij = 0 B
• cij = 0 C
• dij =0 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

• 9/4 A
• 4/9 B
• 1 C
• None of these D

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian D

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

If order of A is m x n, then order of A^tis

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

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

• BA A
• A² B
• AB C
• B² D

• I3 A
• rI3 B
• r C
• none D

(ABC)' =

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

• -a -b -c A
• 1 B
• 0 C
• -1 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

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

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

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

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

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

• Hermitian matrix A
• Skew-hermitian matrix B
• Symmetric matrix C
• Identity matrix D

For a square matrix A, if A = At, then A is called

• Matrix A
• Transpose B
• Symmetric C
• Non-symmetric D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

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

Matrix multiplication is

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

• 0 A
• abc B
• 1/abc C
• None of these D