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iloveannaw
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Homework Statement
show whether the following set of vectors [tex]M = \left\{\left(a_{1},a_{2},a_{3}\right) with a_{1},a_{2},a_{3} \in \Re\right\}[/tex]
with the following limitations:
1) a1 is rational
2) a1 = 0
3) a1 + a2 = 0
4) a1 + a2 = 1
is a vector space over the field of real numbers.
Homework Equations
various axioms
* x+y = y+x.
* (x+y)+z = x+(y+z).
* 0+x = x+0 = x.
* (-x) + x = x + (-x) = 0.
For every x in X and real numbers c,d, we have
* 0x = 0
* 1x = x
* (cd)x = c(dx)
* c(x+y) = cx + cy.
* (c+d)x = cx +dx.
The Attempt at a Solution
I just don't get it, I really wish I could. I understand the axioms but when I apply them i find that M is a vector space regardless of the limitations.
somebody please help
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