Linear Combination - Are these solutions wrong?

pyroknife · Jan 27, 2015

Step 3 of a row reduction of the augmented matrix with rows [1 1 | 1], [a b | c], [a^2 b^2 | c^2], showing the elimination steps that lead to a row with entries 0, b-a, c-a and a row with 0, b^2-a^2, c^2-a^2.

I, II represent rows 1 and 2, respectively.

I am not agreeing with these solutions at step 3 of 5, where they multiply row 2 by 1/(b-a). Correct me if I'm wrong, but we do not know if b-a=0, so I do not think we can divide row II by (b-a) because of the potential of dividing by 0?

What do you guys think?

Mark44 · Jan 27, 2015

pyroknife said:

I, II represent rows 1 and 2, respectively.

I am not agreeing with these solutions at step 3 of 5, where they multiply row 2 by 1/(b-a). Correct me if I'm wrong, but we do not know if b-a=0, so I do not think we can divide row II by (b-a) because of the potential of dividing by 0?

What do you guys think?

I agree with you. From the given information, we can't say that b - a ≠ 0.

Linear Combination - Are these solutions wrong?

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