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

A matrix with a single column is called

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

• 
  A
• 
  B
• 
  C
• 
  D

(ABC)' =

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

If A and B are two matrices such that AB = B and BA =A, then A²+ B²=

• 2 AB A
• 2 BA B
• A + B C
• AB D

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

If there are m rows and n columns in a matrix then its order is

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

The order of the matrix A is 3 x 5 and that of B is 2 x 3.The order of the matrix BA is

• 2 x 3 A
• 3 x 2 B
• 2 x 5 C
• 5 x 2 D

The transport of a square matrix is a

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

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

• BA A
• A2 B
• AB C
• B2 D

• 
  A
• 
  B
• 
  C
• all are correct D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

• 
  A
• 
  B
• 
  C
• 
  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

For non-trival solution |A| is

• A = 0 A
• A^t= 0 B
• |A| = 0 C
• None of these D

• -a -b -c A
• 1 B
• 0 C
• -1 D

• (2x4) A
• (2x7) B
• (2x3) C
• (7x2) D

For non-trival solution |A| is

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

• K/6 A
• 2K B
• 3K C
• 6K D

The transpose of a row matrix is a ______

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

A diagonal matrix is always

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

• 
  A
• 
  B
• 
  C
• 
  D

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

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

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

• -3 A
• -7 B
• 1 C
• 0 D

• 0 A
• 1 B
• 2 C
• 3 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

For trival solution |A| is

• A A
• |A| is non zero B
• A = 0 C
• None of these D

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