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The task is that I have to determine whether this statement is true, to prove my guess by an example, and to explain why:

Given a matrix A, then: To multiply a row in matrix A by a scalar k is the same as dividing some row by a nonzero scalar.

I guess the statement is correct. And I think it's because instead of multiply a row by a scalar k, I could just divide that row by 1/k ...

But somehow I think my thought is too "good". I think if they go thru the trouble of asking me to explain, then there maybe something more to it. I guess the words "some row" somewhat confuse me. Also, I'm assuming that by how they ask the question, I'm not allowed to switch or to add any 2 rows. So I can't use the idea of pivoting ...

So would someone please tell me if my thought is correct?
Thank you very much ^_^

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up vote 2 down vote accepted

Yes, your thought is correct, as specified, because $\,k\neq 0$.

As you say: multiplying a row by a non-zero scalar $k$ is precisely equivalent to dividing a row by the reciprocal of $k\neq 0,\;$ i.e., dividing the row by $\;\dfrac{1}{k}.$

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The way is complete. +1 – Babak S. Feb 11 '13 at 6:01

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