Hello i need help on number 1,2,3,4,5 and 6.
1 answer:
You might be interested in
Answer:
No, those vectors do not span P₂
Step-by-step explanation:
At first, notice we have 4 vectors from a vector space of dimension 3 ({1,x,x²} is the standard base of P₂) so we are sure they are linearly dependent (because there are more than 3 vectors) i.e. it´s possible to write one of them in terms of other in the same set:
p4=p1-p2
Now, we conclude the span {p1,p2,p3,p4} = {p1,p2,p3}
If we want to know the subspace that this span gets, we work with the matrix of the vectors made as follows:
The row-reduction of this matrix show us the basis of the same row-subspace even in the case that some of them are linearly dependent:
This shows that the span {p1,p2,p3}={(1+0.5x²),(x-1.5x²)}
Looking in the previous equality, the span {p1,p2,p3} is generated by two linearly independent vectors, but P₂ needs 3 linearly independent vectors to be generated.
The answer is that {p1,p2,p3,p4}⊂P₂.
Answer:
Step-by-step explanation:
Let p be the population proportion for the graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation.
Given : Tristan is an administrator for a private nonprofit college and read a surprising statistic that 74% of graduates from private nonprofit colleges in the region had at least one outstanding student loan at the time of graduation.
i.e.
He believes that percentage is high and claims that the proportion of graduates at his college is less than the regional rate.
i.e.
Since, the null hypothesis is a statement which always takes equal sign or generally shows " no difference " where as alternative hypothesis takes unequal signs.
Then, the null and alternative hypotheses for this hypothesis test :-