Max, a carpet installer, needs to calculate the amount of carpet needed to cover a floor that’s 3 1⁄2 yards wide and 4 3⁄4 yards
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Answer:
Step-by-step explanation:
The question to be solved is the following :
Suppose that a and b are any n-vectors. Show that we can always find a scalar γ so that (a − γb) ⊥ b, and that γ is unique if . Recall that given two vectors a,b a⊥ b if and only if
where
is the dot product defined in
. Suposse that
. We want to find γ such that
. Given that the dot product can be distributed and that it is linear, the following equation is obtained
Recall that are both real numbers, so by solving the value of γ, we get that
By construction, this γ is unique if , since if there was a
such that
, then