Reference no: EM131026810
Let P be the set of all polynomials. Show that P, with the usual addition and scalar multiplication of functions, forms a vector space.
I'm just no good at proofs. I know we are supposed to go through and prove the Vector Space Axioms and the C1 and C2 closure properties. I just don't think I'm doing it successfully. I'm just not understanding this. For instance, the closure properties don't seem very different from a couple of the axioms.
Axioms:
A1. x + y = y + x for any x and y in V.
A2. (x + y) + z = x + (y + z) for any x,y,z in V.
A3. There exists an element 0 in V such that x + 0 = x for each x in the set V.
A4. For each x in the set V, there exists an element -x in V such that x + (-x) = 0.
A5. alpha(x + y) = alpha*x + alpha*y for each scalar alpha and any x and y in V.
A6. (alpha + beta)x = alpha*x + beta*x for any scalars alpha and beta and any x that belongs to the set V.
A7. (alpha*beta)x = alpha(beta*x) for any scalars alpha and beta and any x that belongs to the set V.
A8. 1*x = x for all x in V.
Closure properties:
C1: If x is in V and alpha is a scalar, then alpha*x is in V.
C2. If x,y is in V, then x + y is in V.
|
Analyse the structural performance of a simple structure
: Assessment task aims to introduce students to FEA and its application in CAE. You will be required to numerically analyse the structural performance of a simple structure
|
|
How should the university report the 280000 of receipts in
: A private university received $280,000 from student tuition and fees for the year 20X9 summer session. The session began on June 20, 20X9, and ended on July 30, 20X9. The university's fiscal year end is June 30. According to the AICPA College and Uni..
|
|
Would you expect water to obey trouton rule
: Calculate ?Svap for each of the liquids. Do all the liquids obey Trouton's rule? With reference to intermolecular forces, can you explain any exceptions to the rule?
|
|
Evaluates the competitive environment for your product
: Write a paper of no more than 1,050 words that evaluates the competitive environment for your product (samsung cell phones) using the Porter's five forces model.
|
|
Addition and scalar multiplication of functions forms vector
: I'm just no good at proofs. I know we are supposed to go through and prove the Vector Space Axioms and the C1 and C2 closure properties. I just don't think I'm doing it successfully. I'm just not understanding this. For instance, the closure prope..
|
|
Significant problem for the business
: Is the fact that Bongo's does not charge for 10% of its pizzas a significant problem for the business? How much extra profit per pizza would be made if 5 minutes was cut from all deliveries?
|
|
What is the value of the critical value of t
: If you were constructing a 99% confidence interval of the population mean based on a sample of n where the standard deviation of the sample s = 0.05, what is the value of the critical value of t that you should use? Explain/show how you obtain your a..
|
|
Show x and y are orthogonal with respect to inner product
: Using this equation with weight vector w=(1/4,1/2,1/4)^t to define an inner product for R^3 and let x=(1,1,1)^T and y=(-5,1,3)^T
|
|
What specifically is difference between given two sections
: Is there more of a feeling of completion in the Recapitulation? What specifically is the difference between the two sections?
|