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Im posting this question since this user is not active for many years

I have some confusion in the given answer Here

My doubt given below marked in red line

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My doubt : we know that 3rd row is linearly independent from first and second row that implies it cannot be linear combination $u_1$ and $u_2$

But here im not getting that

Why its is a linear combination of $u_1 $ and $u_2$?

jasmine
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    It is not a linear combination of $u_1,u_2$. That is what the text says – 1123581321 Oct 09 '20 at 12:42
  • @ΓιάννηςΠαπαβασιλείου NOT word is not mention in given answer – jasmine Oct 09 '20 at 12:43
  • I'm sorry but I don't get your question. Do you think that the answer you refer to is wrong? – 1123581321 Oct 09 '20 at 12:45
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    The text says that $u_3$ can be anything apart from a linear combination of $u_1,u_2$. So $u_3$ is not a linear combination of $u_1,u_2$ – 1123581321 Oct 09 '20 at 12:46
  • okss may be my english is weak @ΓιάννηςΠαπαβασιλείου but it should be written like this...... the third row can be anything but not a linear combination of $u_1$ and $u_2$....Here i have add no word – jasmine Oct 09 '20 at 12:49
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    Yes it is a matter of expression. The way it is writen may be confusing for someone not native english speaker (like me and you) but it is correct – 1123581321 Oct 09 '20 at 12:50
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    https://english.stackexchange.com/questions/8061/what-is-the-difference-between-nothing-but-anything-but-and-everything-bu – Hans Lundmark Oct 09 '20 at 13:47
  • thanks u @HansLundmark now got its.... my english is weak – jasmine Oct 09 '20 at 13:56

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The point is that we want the matrix to be non-singular, so we can't have any of the rows being linearly dependent. For the first three rows not to be linearly dependent translates into the third row not being a linear combination of the first two. Etc...