# Rank of Matrix MCQ

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

1. 1
2. 2
3. 3
4. 0

2. The rank of the matrix is

1. 0
2. 1
3. 2
4. 3

3. The rank of the matrix is 1. 4
2. 1
3. 2
4. 3

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

1. 0
2. 1
3. n – 1
4. 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

1. N/2
2. N – 1
3. N
4. 2N

6. The rank of the matrix is

1. 1
2. 3
3. 2
4. 0

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

1. Q will have four linearly independent rows and four linearly independent columns
2. Q will have four linearly independent rows and five linearly independent columns
3. QQT will be invertible
4. 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?

1. AA’A= A
2. (AA’)2 = A
3. AA’A = I
4. AA’A = A’

9. X = [x1, x2, …….., xn]T is an n-tuple non-zero vector. Then n x n matrix V = XXT

1. has rank zero
2. has rank 1
3. is orthogonal
4. has rank n

10. The rank of the matrix is

1. 0
2. 1
3. 2
4. 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

1. 4
2. 1
3. 2
4. 3

12. Given matrix , the rank of the matrix is

1. 4
2. 2
3. 1
4. 3

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

1. rank of ATA is less than 2.
2. rank of ATA is equal to 2.
3. rank of ATA is greater than 2.
4. rank of ATA can be any number between 1 and 3.

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