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 = [aij], 1 ≤ i, j ≤ n with n ≥ 3 and aij = 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
- QQT will be invertible
- QTQ will be invertible
8. A is m x n full matrix with m > n and I is an identity matrix. Let matrix A’= (ATA)-1 AT, then which one of the following statements is true?
- AA’A= A
- (AA’)2 = A
- AA’A = I
- AA’A = A’
9. X = [x1, x2, …….., xn]T is an n-tuple non-zero vector. Then n x n matrix V = XXT
- 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 ATA is less than 2.
- rank of ATA is equal to 2.
- rank of ATA is greater than 2.
- rank of ATA can be any number between 1 and 3.