The Pythagorean Theorem states that 
, where a and b are the legs of a right triangle and c is the hypotenuse of the same triangle.
The Springfield School band has 300 sweatshirts to sell at the fund-raiser.A survey shows that 2 out of 7 students in the school
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No, 
is not a subspace of 
. A simple counter-example to the contrary: let 
with 
. However, scaling by -1 gives the vector 
and 
.