1. Understanding physical principles is often very useful in everyday life. For example, a skater develops an intuitive understanding of angular momentum in order to master making turns, and virtually all of us as car drivers come to understand the principles of inertia, velocity, and linear momentum. Can you name at least 2 everyday situations where physics plays a role and what physical principles are involved?

2. What is the difference between a vector and scalar distance? Name at least 2 examples from everyday life where each is used.

3. What is the difference between speed and velocity? between velocity and acceleration? Name at least one example from everyday life where each of these concepts (speed, velocity, acceleration) is important (3 total).

Solution Preview

The solution is attached below (next to the paperclip icon) in two formats. one is in Word XP Format, while the other ...

Solution Summary

The solution is a detailed explanation of scalar and vector operations. The solution is step by step in two different formats. The solution also contains helpful links for further studies.

Consider R2 with the following rules of multiplications and additions: For each x=(x1,x2), y=(y1,y2):
x+y=(x2+y2,x1+y1) and for any scalar alpha, alpha*x=(alpha*x1, alpha*x2)
Is it a vector space, if not demonstrate which axioms fail to hold. Also, show that Pn- the space of polynomials of order less than n is a vector spac

Please help with the following problem.
I need help to write this Proof. Please be as professional and as clear as possible in your response. Pay close attention to instructions.
Determine if the set R^2 (the real plane) is a vector space with operations defined by the following:
Addition: (a,b)+(c,d)=(a+c,b+d)
Sca

Define vectors pace and subspace with examples.
State and prove a necessary and sufficient condition for a subset of vectors to be a subspace.
Show that the intersection and union of two sub spaces are also sub spaces.

Give a demonstration as to why or why not the given objects are vector subspaces of M22
a) all 2 X 2 matrices with integer entries
A vector space is a set that is closed under finite vector addition andscalar multiplication.
It is not a vector space, since V is NOT closed under finite scalar multiplication. For insta

Given the set of objects and the operations of addition andscalar multiplication defined in each example below do the following:
Determine which sets are vector spaces under the given operations
For those sets that fail give the axiom(s) that fail to hold
1. The set of all triples of real numbers(x, y, z) with the op

1)Let V be the space of all functions from R to R. It was stated in the discussion session that this is a vector space over R. Prove axioms (VS1)=For all x,y, x+y=y+x (commutativity of addition), (VS3)= There exist an element in V denoted by 0 such that x+0=x for each x in V.,(VS4)= For each element x in V there exist an element

Let P be the set of all polynomials. Show that P, with the usual addition andscalar 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