ECAT Pre Engineering Mathematic MCQ Test With Answer for Chapter 5 (Matrices and Determinants)

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

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

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

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

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

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

Cofactor of an element aij denoted by Aij is

• (-2)i+j A
• Mij B
• (-1)i+j Mij C
• None of above D

• 
  A
• 
  B
• 
  C
• 
  D

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

• 0 A
• 1 B
• 2 C
• 3 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

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

• At Bt A
• AB B
• -AB C
• BA D

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

• 
  A
• 
  B
• 
  C
• 
  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

• 
  A
• 
  B
• 
  C
• 
  D

The transpose of a row matrix is a ______

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

An equation of the form ax + by = k is homogeneous linear equation when

• b = 0, a = 0 A
• a = 0,b ≠ 0 B
• b = -0,a≠ 0 C
• a≠ 0,b≠ 0, k = 0 D

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

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

The square matrix A is skew Hermitian when (A)'=

• A A
• A' B
• -A C
• A 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

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

• I3 A
• rI3 B
• r C
• none D

• 
  A
• 
  B
• 
  C
• all are correct 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

• 1 A
• -1 B
• 0 C
• I D

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

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

If A is singular then |A| = ______

• 1 A
• 0 B
• 2 C
• None of these 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