Find a basis for the space of polynomials p(x) having degree at most 3. Find a basis for the subspace of polynomials p(x) having degree at most 3 with p(1)

Where a,b,c,d represent constants.

For case given we have this:

And we need that

That's satisfied if

Where

So then a possible basis for this case would be:

And we can check that the spans for the subspace is linearly independent.

Step-by-step explanation:

We want to find a basis for the subspace of all polynomials with degree and we need to satisfy the condition that

Our general expression for an element of the space described above is given by this equation:

Where a,b,c,d represent constants.

For case given we have this:

And we need that

That's satisfied if

So we want a basis for the subsapce of all the polynomials on this form:

Where

So then a possible basis for this case would be:

And we can check that the spans for the subspace is linearly independent.

(2,20) means that the 2 is 2 hours and 20 is 20$. so there both 20$ for 2 hours only the same price. like it says. so, the dunk tank and the bounce house are the same price (20$) for the same amount of time (2 hours).

hope i

in the attachment.   i didn't see your choices.   the word which means there is choices.

step-by-step explanation:

(x,y)

x tells you how much left or right you go from the origin

y tells you how much down or up you go from the origin

so for example (-3,2), you go left 3 and up twice. i denoted which of the ordered pairs is which in my graph.