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BillhB

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Mpost moved from the technical math forums, so no HH Template is shown.

Hey all, student100's brother here, he got me to create an account to ask my question here...

I'm taking an introduction to linear algebra class and we had a test problem to prove a set of vectors is linear independent: ##V = v_1, \dots, v_n \in \Bbb R^n## such that each element of the set is orthogonal to each other, or ## v_1 \cdot (v_2,\dots, v_n)= 0##.

Now I realize I could have just used that to prove that linear independence by adding c's in front of each term and following the logic, but on the test the first thing that came to mind was to suppose another set ##W= v_n, \dots, v_1 \in \Bbb R^n## and then show that $$C_1V+C_2W=0$$ $$(C_1V+C_2W)\cdot V=0\cdot V$$ $$C_1V \cdot V+C_2W \cdot V=0$$ $$C_1V^2+0=0$$

Therefore ##C_1## = 0, I then did the same thing with ##C_2## to show ##C_1=C_2=0## and that V is linear independent. Whats wrong with this proof? The professor said it wasn't general enough, and to be fair didn't take full credit because he said I had the right idea. I just don't understand the "not general enough part." I've never taken a proof based math course, so as you can imagine it's not going hot.

Hopefully this makes sense.

The book we're using if that helps is Anton linear algebra 7th edition.

I'm taking an introduction to linear algebra class and we had a test problem to prove a set of vectors is linear independent: ##V = v_1, \dots, v_n \in \Bbb R^n## such that each element of the set is orthogonal to each other, or ## v_1 \cdot (v_2,\dots, v_n)= 0##.

Now I realize I could have just used that to prove that linear independence by adding c's in front of each term and following the logic, but on the test the first thing that came to mind was to suppose another set ##W= v_n, \dots, v_1 \in \Bbb R^n## and then show that $$C_1V+C_2W=0$$ $$(C_1V+C_2W)\cdot V=0\cdot V$$ $$C_1V \cdot V+C_2W \cdot V=0$$ $$C_1V^2+0=0$$

Therefore ##C_1## = 0, I then did the same thing with ##C_2## to show ##C_1=C_2=0## and that V is linear independent. Whats wrong with this proof? The professor said it wasn't general enough, and to be fair didn't take full credit because he said I had the right idea. I just don't understand the "not general enough part." I've never taken a proof based math course, so as you can imagine it's not going hot.

Hopefully this makes sense.

The book we're using if that helps is Anton linear algebra 7th edition.