Question

the rank of a matrix of order m×n is​

Answer 1

Answer:

The rank of a matrix is the dimension of the subspace spanned by its rows. ... For any m × n matrix, rank (A) + nullity (A) = n. Thus, if A is n × n, then for A to be nonsingular, nullity (A) must be zero.

Answer 2

The rank of a matrix of order m × n is given by 0 < rank of A ≤ min {m, n} where A is a matrix of order m × n

Given :

A matrix of order m × n

To find :

The rank of a matrix of order m × n

Solution :

Step 1 of 2 :

Define rank of a matrix

Let A be a non zero matrix of order m × n. The Rank of A is defined to be the greatest positive integer r such that A has at least one non-zero minor of order r

For a non-zero m × n matrix A

0 < rank of A ≤ min {m, n}

For a non-zero matrix A of order n,

rank of A < , or = n according as A is singular or non-singular

Step 2 of 2 :

Find the rank

Let A be the given matrix

Then rank of the matrix is given by

0 < rank of A ≤ min {m, n}

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