3
linear change of coordinates on R illustrated
New basis: b 1 d 1, 2, 3 : b 2 d 2, 3, 1 : b 3 d 3, 1, 2 :
Below the black vector x = 1, 6, 5 = 2 b 1 C b 2 K b 3 is represented as
twice the red vector plus one times the blue vector minus the one times the
Balancing chemical reactions
How can we balance the following reaction (burning methane gas):
CH4 C O2 / CO2 C H2O ?
Namely how many of each molecule do we need on both sides of the reaction (in and out) so that the number of
atoms of each type does not c
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the 3d vector space of (at most) quadratic expressions in a variable
The space of (at most) quadratic functions in a single variable x is a 3-dimensional vector space: the sum of two
quadratics is a quadratic whose ordered coefficients are the sum of the
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signs when
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