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

• At A
• -A B
• A C
• A-1 D

• 
  A
• 
  B
• 
  C
• 
  D

Matrix multiplication is

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

Cofactor of an element a_ijis defined by

• (-1)^i+j|A| A
• (-1)^i+jM_ij B
• (-1)^i+jM^-1 C
• None of these D

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

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

• A2 A
• A3 B
• A C
• None of above D

The matrix A = [aij]1xn is a

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

• I3 A
• rI3 B
• r C
• none 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

Trival solution of homogeneous linear equation is

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

• 
  A
• 
  B
• 
  C
• 
  D

If A is skew Hermitian Matrix then which of the following is not skew Hermitian matrix

• A2 A
• A5 B
• A3 C
• A7 D

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 
  A
• 
  B
• 
  C
• 
  D

Let A is a 3 x 3 matrix and B is its adjoint matrix. If |B| = 64, then |A| =

• 
  A
• 
  B
• 
  C
• 
  D

The transport of a rectangular matrix is a

• Square matrix A
• Rectangular matrix B
• Row matrix C
• Column matrix D

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

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

• a = -1/2, b = -1 A
• a = 1, b = 2 B
• a = 2, b = 3 C
• None of above D

• 0 A
• 1 B
• 2 C
• 4 D

In order of A is m x n and order of B is n x p then order of AB is

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

The transpose of a row matrix is a ______

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

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

• 
  A
• 
  B
• 
  C
• 
  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 square matrix all of whose elements except the main diagonal are zeros is called a

• Null matrix A
• Singular matrix B
• Symmetric matrix C
• Diagonal matrix D

A = [3] is a/an

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