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

The transpose of a column matrix is a ______

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

• k3 A
• 0 B
• 3k C
• k6 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

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

• An upper triangular matrix A
• A lower triangular matrix B
• A diagonal matrix C
• A null matrix D

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

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

• Hermitian matrix A
• Skew-hermitian matrix B
• Symmetric matrix C
• Identity matrix D

• K/6 A
• 2K B
• 3K C
• 6K D

For non-trival solution |A| is

• non zero A
• A = 0 B
• |A| = 0 C
• At = 0 D

• At A
• -A B
• A C
• A-1 D

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

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

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

A matrix with a single row is called a

• Column matrix A
• Row matrix B
• Null matrix C
• Identity matrix 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 matrix with a single column is called

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

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

Rank of matrix [1 3 5 0] is

• 1 A
• 3 B
• 2 C
• 4 D

We also 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

A and B be two square matrices and if their inverse exist the (AB)-1 =

• A-1 B-1 A
• AB-1 B
• A-1B C
• B-1A-1 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

The square matrix A is skew-symmetric when At =

• -B A
• -C B
• -A C
• -D D

• Null matrix A
• Triangular matrix B
• Unit matrix C
• Rectangular matrix D

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

• A² A
• A³ B
• A C
• None of above D

• x =0, y =4 A
• x = -1, y = 2 B
• x = 2, y = 3 C
• x = 3, y = 4 D

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

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

• A2 A
• A3 B
• A C
• None of above D

• A A
• -A B
• A^t C
• A^- D