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 of 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 between 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...

3. Prove or disprove the following statement: If A and B are
finite sets, then |A ∪ B| = |A| + |B|.

Prove for each:
a. Proposition: If A is finite and B is countable, then A ∪ B is
countable.
b. Proposition: Every subset A ⊆ N is finite or countable.
[Similarly if A ⊆ B with B countable.]
c. Proposition: If N → A is a surjection, then A is finite or
countable. [Or if countable B → A surjection.]

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)

) 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!!!!

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.

Please first prove A to be a Hermitian operator, and after
please prove <A^2> to be positive.

1) a). Prove or Disprove: "Every random variable has cumulative
distribution". Justify
b). If statement in problem (a) is true, does the existence of
cumulative distributions function of a random variable imply the
existence of probability density function? Justify.

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 35 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago

asked 3 hours ago

asked 3 hours ago

asked 3 hours ago