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

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

• BA A
• A2 B
• AB C
• B2 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

If the matrices A and B are conformable for multiplication then (AB)^t= ______

• AB A
• A^tB^t B
• B^tA^t C
• A^tB D

A diagonal matrix is always

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

• a = 2, b = 3 A
• a = 3, b = 2 B
• a = 2, b = 1, 2 C
• a = 3, b = 3 D

• -a -b -c A
• 1 B
• 0 C
• -1 D

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

Every identity matrix is

• Row-vector A
• Scalar B
• Column-vector C
• All D

• 
  A
• 
  B
• 
  C
• 
  D

• Identity matrix A
• Diagonal matrix B
• Null matrix C
• Hermitian matrix D

Let A be a square matrix. Then, 1/2 (A-A') is

• Skew-symmetric A
• Symmetric B
• Null C
• None of the above D

• 5 A
• 15 B
• 10 C
• 20 D

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

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

• At Bt A
• AB B
• -AB C
• BA D

For non-trival solution |A| is

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

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

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

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

• 1 A
• -1 B
• 0 C
• I D

• 
  A
• 
  B
• 
  C
• 
  D

The matrix A is Hermitian when (A)' =

• A A
• -A B
• A C
• A' D

• 4A - 3I A
• 3A - 4I B
• A - I C
• None of these D

• 0 A
• 1 B
• -A C
• -1 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

• 
  A
• 
  B
• 
  C
• all D

• 2s² A
• 2s³ B
• s³ C
• 3s³ D

The transport of a rectangular matrix is a

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

In order of A is m x n and order of B is n x p then order of AB is

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