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If Rank (A) = 2 and Rank (B) = 3, then Rank (AB) is __________.
  • a)
    6
  • b)
    5
  • c)
    3
  • d)
    Data inadequate
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
If Rank (A) = 2 and Rank (B) = 3, then Rank (AB) is __________.a)6b)5c...
Explanation:

The rank of a matrix refers to the maximum number of linearly independent rows or columns in the matrix.

When we multiply two matrices A and B, the rank of the resulting matrix AB can be less than, equal to or greater than the ranks of matrices A and B.

However, we cannot determine the rank of AB solely based on the ranks of A and B. We also need information about the dimensions and entries of A and B to determine the rank of AB.

Therefore, the answer to this question is "data inadequate" as we do not have enough information to determine the rank of AB.
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Community Answer
If Rank (A) = 2 and Rank (B) = 3, then Rank (AB) is __________.a)6b)5c...
Given,
ρ(A) = 2
ρ(B) = 3
Rank: The rank of a matrix is a number equal to the order of the highest order non-vanishing minor, that can be formed from the matrix.
For matrix A, it is denoted by ρ(A).
The rank of a matrix is said to be r if, there is at least one non-zero minor of order r.
Every minor of matrix A having an order higher than r is zero.
Property of Rank of matrix:
ρ(AB) ≤ min[ρ(A), ρ(B)]
The rank of a matrix does not change by elementary transformation, we can calculate the rank by changing the matrix into Echelon form. In the Echelon form, the rank of a matrix is the number of non-zero rows of the matrix.
The rank of a matrix is zero if the matrix is null.
The rank of a skew-symmetric matrix cannot be one.
Using properties,
ρ(AB) ≤ min[ρ(A), ρ(B)]
ρ(AB) ≤ min(2,3)
⇒ ρ(AB) ≤ 2
∴ We don't know the dimension of A and B, we cannot predict the exact rank of AB but its maximum rank will be 2.
Hence, the correct option is (D).
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Consider the relation account (customer, balanc e) where customer is a primary key and there are no null values. We would like to rank customers according to decreasing balance. The customer with the largest balance gets rank 1. ties are not broke but ranks are skipped: if exactly two customers have the largest balance they each get rank 1 and rank 2 is not assignedConsider these statements about Query1 and Query2.1. Query1 will produce the same row set as Query2 for some but not all databases.2. Both Query1 and Query2 are correct implementation of the specification3. Query1 is a correct implementation of the specification but Query2 is not4. Neither Query1 nor Query2 is a correct implementation of the specification5. Assigning rank with a pure relational query takes less time than scanning in decreasing balance order assigning ranks using ODBC.Q.Which two of the above statements are correct?

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If Rank (A) = 2 and Rank (B) = 3, then Rank (AB) is __________.a)6b)5c)3d)Data inadequateCorrect answer is option 'D'. Can you explain this answer?
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