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

The transport of a square matrix is a

• Row matrix A
• Column matrix B
• Square matrix C
• Null matrix 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

• 16 A
• 256 B
• 64 C
• 1024 D

• 5 A
• 
  B
• -5 C
• none D

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

• BA A
• A² B
• AB C
• B² D

If A = [aij]mxpand B =[aij]pxnthen order of BA is

• m x n A
• p x n B
• n x m 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

• 2s² A
• 2s³ B
• s³ C
• 3s³ 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

• 
  A
• 
  B
• 
  C
• 
  D

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

• 1, 2, 3 A
• 1, 5, 9 B
• 2, 5, 8 C
• 3, 6, 9 D

• 
  A
• 
  B
• 
  C
• 
  D

• 
  A
• 
  B
• 
  C
• 
  D

• 0 A
• 1 B
• 2 C
• 3 D

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

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

• 
  A
• 
  B
• 
  C
• 
  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

We solve the system of non-homogeneous linear equations by

• a and b A
• b and c B
• c and a C
• a,b and c D

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

The transpose of a row matrix is a ______

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

A matrix with a single row is called a

• Column matrix A
• Row matrix B
• Null matrix C
• Identity matrix D

The additive inverse of a matrix A is

• 
  A
• 
  B
• 
  C
• None of these 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

Trival solution of homogeneous linear equation is

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

• Symmetric A
• Skew-symmetric B
• Hermitian C
• Skew hermitian 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 for which A^t= A is called a

• Column matrix A
• Symmetric matrix B
• Skew-symmetric matrix C
• Row matrix 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

For trival solution |A| is

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