Question

If A is a 6 × 9 matrix what is the maximum possible rank of A? What is the minimum possible rank of A ?

Answer 1

Largest possible rank =6

Minimum possible rank=0

Explanation:

We are given that A is a matrix of order
`6* 9`

We have to find the maximum possible rank and minimum possible rank of A.

In given matrix we have 6 rows and 9 columns.

Rank: Rank is defined as the number of non zero rows or columns of matrix and any row or column is not a linear combination of other two or more rows or columns

Rank of matrix of order
`m* n`

Where m< n

Then largest possible rank is m

We are given a matrix of order
`6* 9` where 6< 9

Therefore, the largest possible rank is 6.

The minimum possible rank is zero because a given matrix can be zero matrix therefore, the rank of zero matrix is zero.

Largest possible rank =6

Minimum possible rank=0