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Ok so I am reading a book on linear algebra ( Gilbert Strang to be specific) and I am on second problem set, challenge problem, problem 29. In solutions it appears that the author states that:

$$x\cdot y=xz+yz+xy=(1/2)(x+y+z)^2 - (1/2)(x^2 + y^2 + z^2)$$

How is that possible?

Dan Rust
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Vanio Begic
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    The second equality is algebra. The first would depend on definitions in the problem, but it seems odd to use the letters $x,y$ seemingly as vectors (for dot product) and also as components of the vectors (in the expression $xz+yz+xy$). – coffeemath Nov 08 '13 at 01:41

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