Question

**Choose one of the following problems and determine
whether the given set (together with the usual operations on that
set) forms a vector space over R. In all cases, justify your answer
carefully.**

a. The set of all n x n matrices A such that A² is symmetric.

b. The set of all points in **R****²**
that are equidistant from (-1, 2) and (1, -2)

c. The set of all polynomials of degree 5 or less whose coefficients of x² and x³ are zero.

you can choose any

Answer #1

Determine if the given set V is a subspace of the vector space
W, where
a) V={polynomials of degree at most n with p(0)=0} and W=
{polynomials of degree at most n}
b) V={all diagonal n x n matrices with real entries} and W=all n
x n matrices with real entries
*Can you please show each step and little bit of an explanation
on how you got the answer, struggling to learn this concept?*

Prove that the set V of all polynomials of degree ≤ n including
the zero polynomial is vector space over the field R under usual
polynomial addition and scalar multiplication. Further, find the
basis for the space of polynomial p(x) of degree ≤ 3. Find a basis
for the subspace with p(1) = 0.

Indicate whether each statement is True or False.
Briefly justify your answers. Please answer all of questions
briefly
(a) In a vector space, if c⊙⃗u =⃗0, then c= 0.
(b) Suppose that A and B are square matrices and that AB is a
non-zero diagonal matrix. Then A is non-singular.
(c) The set of all 3 × 3 matrices A with zero trace (T r(A) = 0)
is a vector space under the usual matrix operations of addition and
scalar...

Determine whether the given set ?S is a subspace of the vector
space ?V.
A. ?=?2V=P2, and ?S is the subset of ?2P2
consisting of all polynomials of the form
?(?)=?2+?.p(x)=x2+c.
B. ?=?5(?)V=C5(I), and ?S is the subset of ?V
consisting of those functions satisfying the differential equation
?(5)=0.y(5)=0.
C. ?V is the vector space of all real-valued
functions defined on the interval [?,?][a,b], and ?S is the subset
of ?V consisting of those functions satisfying
?(?)=?(?).f(a)=f(b).
D. ?=?3(?)V=C3(I), and...

Are the following vector space and why?
1.The set V of all ordered pairs (x, y) with the addition of
R2, but scalar multiplication a(x, y) = (x, y) for all a
in R.
2. The set V of all 2 × 2 matrices whose entries sum to 0;
operations of M22.

Show that the set GLm,n(R) of all mxn matrices with
the usual matrix addition and scalar multiplication is a finite
dimensional vector space
with dim GLm,n(R) = mn.
Show that if V and W be finite dimensional vector spaces with
dim V = m and dim W = n, B a basis for V and C a basis for W
then
hom(V,W)-----MatB--->C(-)-------->
GLm,n(R) is a bijective linear transformation. Hence or
otherwise, obtain dim hom(V,W).
Thank you!

The trace of a square n×nn×n matrix A=(aij)A=(aij) is the sum
a11+a22+⋯+anna11+a22+⋯+ann of the entries on its main
diagonal.
Let VV be the vector space of all 2×22×2 matrices with real
entries. Let HH be the set of all 2×22×2 matrices with real entries
that have trace 11. Is HH a subspace of the vector space
VV?
Does HH contain the zero vector of VV?
choose H contains the zero vector of V H does not contain the zero
vector...

________ client-centered therapy centers on the patient's goals
and ways of solving problems.
Select one:
a. Rogers'
b. Freud's
c. Beck
d. Ellis
Question 2
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Question text
A frequently prescribed drug therapy for managing one's
depression is ____________.
Select one:
a. Adderall
b. Lithium
c. Prozac
d. Thorazine
Question 3
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A major goal of modern inpatient psychiatric treatment is:
Select...

MK Restaurant: Branding of Thai-Style Hotpot
The restaurant industry is one of the most competitive in
Thailand. With a large number of players ranging from restaurants
in five-star hotels, global fast-food chains to small stalls along
the streets and everything in between, the Thais are spoiled for
choice. In addition, as the world becomes globalized, consumers are
familiar with international dishes and would not hesitate to try
new offerings from the other side of the globe. As a...

What tools could AA leaders have used to increase their
awareness of internal and external issues?
???ALASKA AIRLINES: NAVIGATING CHANGE
In the autumn of 2007, Alaska Airlines executives adjourned at
the end of a long and stressful day in the
midst of a multi-day strategic planning session. Most headed
outside to relax, unwind and enjoy a bonfire
on the shore of Semiahmoo Spit, outside the meeting venue in
Blaine, a seaport town in northwest
Washington state.
Meanwhile, several members of...

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