The quotient of two negative integersis
2 answers:
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Given the dataset
We start by computing the average:
We compute the difference bewteen each element and the average:
We square those differences:
And take the average of those squared differences: we sum them
And we divide by the number of elements:
Finally, we take the square root of this quantity and we have the standard deviation:
The span of 3 vectors can have dimension at most 3, so 9 is certainly not correct.
Check whether the 3 vectors are linearly independent. If they are not, then there is some choice of scalars (not all zero) such that
which leads to the system of linear equations,
From the third equation, we have , and substituting this into the second equation gives
and in turn, . Substituting these into the first equation gives
which tells us that any value of will work. If
, then
and
. Therefore the 3 vectors are not linearly independent, so their span cannot have dimension 3.
Repeating the calculations above while taking only 2 of the given vectors at a time, we see that they are pairwise linearly independent, so the span of each pair has dimension 2. This means the span of all 3 vectors taken at once must be 2.