Question

2. Please justify and prove each statement

a) Prove that a finite positive linear combination of metrics is a metric. If it is infinite, will it be metric?

b) Is the difference between two metrics a metric?

Answer #1

2. Please justify and prove each statement
a) Prove that a finite positive linear combination of metrics is
a metric. If it is infinite, will it be metric?
b) Is the difference of two metrics a metric?

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...

) Let L : V → W be a linear transformation between two finite
dimensional vector spaces. Assume that dim(V) = dim(W). Prove that
the following statements are equivalent. a) L is one-to-one. b) L
is onto.
please help asap. my final is tomorrow morning. Thanks!!!!

Prove why the following statement is true:
A determinant is linear as a function of each of its vector
arguments.

To form a linear combination of two things, you multiply each by
a constant and then add the result together. For example, 2x+3y,
-x+4y, ex-πy, 0x+0y are all linear combinations of x and y. -3y is
even a linear combination of x and y because 0x-3y=-3y. Which of
the following are linear combinations of a and b? Select all that
apply.
2a-5b
ab+b
3a
b-a
2a^(2)-3b^(2)

Answer each of the following as True or False:
In a linear correlation testing, any positive value for the
linear correlation coefficient (r) statistic always indicates a
positive correlation between the two variables.
The chi-square test for independence is similar to a
correlation in that it evaluates the relationship between two
variables.
It is impossible to obtain a value less than zero for the
chi-square statistic, unless a mistake is made.
In a two-sample t-test, it makes a difference which...

A)
Prove that a group G is abelian iff (ab)^2=a^2b^2 fir any two
ekemwnts a abd b in G.
B) Provide an example of a finite abelian group.
C) Provide an example of an infinite non-abelian group.

Write each vector as a linear combination of the vectors in
S. (Use s1 and s2, respectively, for
the vectors in the set. If not possible, enter IMPOSSIBLE.)
S = {(1, 2, −2), (2, −1, 1)}
(a) z = (−5, −5,
5)
z = ?
(b) v = (−2, −6,
6)
v = ?
(c) w = (−1, −17,
17)
w = ?
Show that the set is linearly dependent by finding a nontrivial
linear combination of vectors in the set whose sum...

Prove that for each positive integer n, (n+1)(n+2)...(2n) is
divisible by 2^n

butadiene (C4H10), the coefficients for the linear combination
of atomic orbitals for the two lowest energy π-MOs are:
Normalised Coefficients MO
Atom
1
Atom 2
Atom 3
Atom 4
Wavefunction 2:
+0.6015
+0.3717
–0.3717
–0.6015
Wavefunction1 : +0.3717
+0.6015
+0.6015
+0.3717
(i) Predict the coefficients at each atom for the two highest
energy π-MOs (wavefunctions 3 & 4). Justify your solution using
diagrams.
(ii) Calculate the total π-electron densities on atoms 1,...

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