Question

If a matrix A has at least one minor of order ris non zero and every​

Answer 1

Answer:

It is denoted by the symbol ρ (A). The rank of a zero matrix is defined to be 0.

(ii) The rank of the identity matrix In is n.

(iii) If the rank of a matrix A is r, then there exists at-least one minor of A of order r which does not vanish and every minor of A of order r + 1 and higher order (if any) vanishes.

Answer 2

If a matrix A has at least one minor of order r is non-zero and every minors of order (r + 1) are zero then Rank of matrix A = r

Given : A matrix A has at least one minor of order r is non-zero and every minors of order (r + 1) are zero

To find : Then

1. Rank of matrix A ≥ r

2. Rank of matrix A = r

3. Rank of matrix A ≤ r

4. None of these

Solution :

We know that for a non zero matrix A 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

Here it is given that the matrix A has at least one minor of order r is non-zero

Since every minors of order (r + 1) are zero

So by the definition of rank of a matrix , rank of A = r

N.B : The question is incomplete. The Complete question is referred to the link : https://brainly.in/question/48774267

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