1. Let be two matrices. Then the rank of P + Q is

- 1
- 2
- 3
- 0

2. The rank of the matrix is

- 0
- 1
- 2
- 3

3. The rank of the matrix is

- 4
- 1
- 2
- 3

4. Let A = [a_{ij}], 1 ≤ i, j ≤ n with n ≥ 3 and a_{ij} = i.j . The rank of A is

- 0
- 1
- n – 1
- n

5. Two matrices A and B are given below:

If the rank of matrix A is N, then the rank of matrix B is

- N/2
- N – 1
- N
- 2N

6. The rank of the matrix is

- 1
- 3
- 2
- 0

7. If the rank of a (5 x 6) matrix Q is 4, then which one of the following statements is correct?

- Q will have four linearly independent rows and four linearly independent columns
- Q will have four linearly independent rows and five linearly independent columns
- QQ
^{T}will be invertible - Q
^{T}Q will be invertible

8. A is m x n full matrix with m > n and I is an identity matrix. Let matrix A’= (A^{T}A)^{-1} A^{T}, then which one of the following statements is true?

- AA’A= A
- (AA’)
^{2}= A - AA’A = I
- AA’A = A’

9. X = [x_{1}, x_{2}, …….., x_{n}]^{T} is an n-tuple non-zero vector. Then n x n matrix V = XX^{T}

- has rank zero
- has rank 1
- is orthogonal
- has rank n

10. The rank of the matrix is

- 0
- 1
- 2
- 3

11. A is a 3 x 4 real matrix and Ax = b is an inconsistent system of equations. The highest possible rank of A is

- 4
- 1
- 2
- 3

12. Given matrix , the rank of the matrix is

- 4
- 2
- 1
- 3

13. Let A be a 4 x 3 real matrix with rank 2. Which one of the following statement is true?

- rank of A
^{T}A is less than 2. - rank of A
^{T}A is equal to 2. - rank of A
^{T}A is greater than 2. - rank of A
^{T}A can be any number between 1 and 3.