Thread: does it change if we multiply a row by a number of an echelon matrix

8 4 7 0 4
4 2 2 6 5
1 6 7 3 2 mod 11
2 1 2 5 0

does this matrix change if we multiply the first row by:

7, we got:

1 6 5 0 6 (mod 11)

?

I am guessing that what you were trying to ask is "Does the matrix after we multiply the first row by 7 have the same row echelon form as the original matrix?"
If I have interpreted your question correctly, then the answer is yes: You can multiply any row by a scalar or add a scalar multiple of a row to another row without changing the row echelon form of the matrix.

If I haven't understood your question, I suggest you clarify it as others are likely having the same trouble

my question is:

the echelon matrix i m asking is on a field of p elements(p is a prime),represented by integers modulo p.

so,
1. does the row space change if i multiply any row by element of F?
2. does the row space change if i subtract(or add) a times any row j from row i,?
3. does the row space change if i transpose row i and j?

1. does the row space change if i multiply any row by element of F?

No.

2. does the row space change if i subtract(or add) a times any row j from row i,?

No, assuming a is an element of the field.

3. does the row space change if i transpose row i and j?

No

Good work, that was much clearer

thank you!