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Math Help - does it change if we multiply a row by a number of an echelon matrix

  1. #1
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    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)

    ?
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  2. #2
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    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
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  3. #3
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    ok

    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?


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  4. #4
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    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
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  5. #5
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    thanks

    thank you!
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