ECAT Pre Engineering MCQ Test With Answer for Chapter 5 Mathematics

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

• A² A
• A³ B
• A C
• None of above D

• 
  A
• 
  B
• 
  C
• 
  D

The transport of a null matrix is

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

• a = 4, b = 1 A
• a = 1, b = -4 B
• a = 0, b = 4 C
• a = 2, b = 4 D

• A(α) - A(β) A
• A(α) + A(β) B
• A(α-β) C
• A(α+β) D

• I3 A
• rI3 B
• r C
• none D

• 0 A
• 1 B
• 2 C
• 3 D

• k3 A
• 0 B
• 3k C
• k6 D

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

• 
  A
• 
  B
• 
  C
• all D

The matrix A = [aij]1xn is a

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

If A is a skew-symmetric matrix of order n and P, any square matrix of order n.prove that P' AP is

• Skew-symmetric A
• Symmetric B
• Null C
• Diagonal D

• 1 A
• 0 B
• 3 C
• -1 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

• 5 A
• 
  B
• -5 C
• none D

If order of A is m x n, then order of A^tis

• m x m A
• n x n B
• m x n C
• n x m D

(ABC)' =

• CBA' A
• CBA B
• C'B'A C
• C'B'A' 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

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

• 
  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

If A is a non singular matrix then A^-1= ______

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

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

• 
  A
• 
  B
• 
  C
• 
  D