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

The matrix A = [aij]1xn is a

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

Matrix multiplication is

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' D

• 6, -12, -18 A
• -6, 4, 9 B
• -6, -4, -9 C
• -6, 12, 18 D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

The transpose of a row matrix is a ______

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

If A is a non-singular matrix then adj A is

• Non-singular A
• Symmetric B
• Singular C
• Non defined 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

Every identity matrix is

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

• 2 A
• 4 B
• 6 C
• 8 D

The order of the matrix [1 2 3] is

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these D

• A²- 5A + 7I = 1 A
• 2A²- 3A + 7I = 0 B
• A²- 5A + I = 0 C
• A²- 5A + 7I = 0 D

• I3 A
• rI3 B
• r C
• none D

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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

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

• K/6 A
• 2K B
• 3K C
• 6K D

• 
  A
• 
  B
• 
  C
• all D

• 
  A
• 
  B
• 
  C
• 
  D

Minor of an element a_ijis denoted by

• M_ij A
• A_ij B
• |A| C
• None of these D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

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

A = [3] is a/an

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

• 
  A
• 
  B
• 
  C
• 
  D

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

• A2 A
• A3 B
• A C
• None of above D

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

• A^- A
• A^t B
• -A C
• A D