ECAT Pre Engineering Mathematic MCQ Test With Answer for 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

• 0 A
• 1 B
• -2 C
• 10 D

System of linear equations is inconsistent if

• System has no solution A
• System has one solution B
• System has two solution C
• None of above D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 
  A
• 
  B
• 
  C
• 
  D

A diagonal matrix is always

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

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' 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

(ABC)' =

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

For trival solution |A| is

• A A
• |A| = 0 B
• A = 0 C
• |A|≠ 0 D

• 
  A
• 
  B
• 
  C
• 
  D

Which of the following is an identity matrix?

• 
  A
• 
  B
• 
  C
• none of these D

• 16 A
• 256 B
• 64 C
• 1024 D

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

• 
  A
• 
  B
• 
  C
• all D

• 
  A
• 
  B
• 
  C
• 
  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

The transpose of a row matrix is a ______

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

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these D

The matrix A = [aij]mxn with m ≠n is always

• Symmetric A
• Hermition B
• Skew-symmetric C
• None 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

• (2x+a+b+c) A
• (a+b+c) B
• (a+b+c+x) C
• 0 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

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

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

• 
  A
• 
  B
• 
  C
• 
  D