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.

total amount to be paid = $19.5

step-by-step explanation:

given ,

original price = $25.99

discount = 25%

discount amount = 25% of original price

discount amount = 25/100   * 25.99

discount amount = $6.49

hence , the total amount to be paid = original price - discount amount

                                                            = $25.99 - $6.49

                                                            =$19.5

total amount to be paid = $19.5