Question

Determine if each of the following statements is true or false. If it’s true, explain why. If it’s false explain why not, or simply give an example demonstrating why it’s false

(a) If λ=0 is not an eigenvalue of A, then the columns of A fo ma basis of R^n.

(b) If u, v ∈ R^3 are orthogonal, then the set {u, u − 3v} is orthogonal.

(c) If S1 is an orthogonal set and S2 is an orthogonal set with S1 ∩S2 = φ, then S1 ∪S2 is an orthogonal set.

Answer #1

Determine if each of the following statements is true or false.
If it’s true, explain why. If it’s false explain why not, or simply
give an example demonstrating why it’s false. (A correct choice of
“T/F” with no explanation will not receive any credit.)
(a) If two lines are contained in the same plane, then they must
intersect.
(c) Let n1 and n2 be normal vectors for two planes P1, P2. If n1
and n2 are orthogonal, then the planes...

Give an counter example or explain why those are false
a) every linearly independent subset of a vector space V is a basis
for V
b) If S is a finite set of vectors of a vector space V and v
⊄span{S}, then S U{v} is linearly independent
c) Given two sets of vectors S1 and S2, if span(S1) =Span(S2), then
S1=S2
d) Every linearly dependent set contains the zero vector

For each of the following short statements, explain whether it
is True or False. If it’s true, explain why. If it’s false, give a
counter-examples or explain why it’s false. (a) (b) (c)
(5 points) Suppose in a game a player has three decision nodes,
with three possible actions at each node: A,B and C. The player has
fewer strategies in a version of the game where C end the game,
than in another version of the game where C...

(6) Label each of the following statements as True or
False. Provide justification
for your response.
(b) True/False The scalar λ is an eigenvalue of a
square matrix A if and
only if the equation (A − λIn)x = 0 has a nontrivial
solution.
(c) True/False If λ is an eigenvalue of a matrix A, then there is
only
one nonzero vector v with Av = λv.
(d) True/False The eigenspace of an eigenvalue of an n × n matrix...

Answer all of the questions true or false:
1.
a) If one row in an echelon form for an augmented matrix is [0 0 5
0 0]
b) A vector b is a linear combination of the columns of a matrix A
if and only if the
equation Ax=b has at least one solution.
c) The solution set of b is the set of all vectors of the form u =
+ p + vh
where vh is any solution...

Determine if the following statements are true or false. If it
is true, explain why. If it is false, provide an example.
a.) If a and b are positive numbers, then (a+b)^x=a^x+b^x
b.) If x < y, then e^x < e^y
c.) If 0 < b <1 and x < y then b^x > b^y
d.) if e^(kx) > 1, then k > 0 and x >0

Are the following statements true or false? Please explain why
it's true or false as well.
For a normally distributed random variable, P(X > µ) = .5
Independent variables may be linearly related

Determine whether the following statements are true or
false. If the statement is false, then explain why the statement is
false or rewrite the statement so that it is true.
If a scatterplot shows a linear association
between two numerical variables, then a correlation coefficient
that is close to 1 indicates a strong positive trend and a
correlation coefficient that is close to 0 indicates a strong
negative trend.

1) (a) Determine if the following statements are true or false.
If true give a reason or cite a theorem and if false, give a
counterexample.
i) If { a n } is bounded, then it converges.
ii) If { a n } is not bounded, then it diverges.
iii) If { a n } diverges, then it is not bounded.
(b) Give an example of divergent sequences { a n } and
{ b n } such that {...

For each of the following statements, say whether the statement
is true or false.
(a) If S⊆T are sets of vectors, then span(S)⊆span(T).
(b) If S⊆T are sets of vectors, and S is linearly independent,
then so is T.
(c) Every set of vectors is a subset of a basis.
(d) If S is a linearly independent set of vectors, and u is a
vector not in the span of S, then S∪{u} is linearly
independent.
(e) In a finite-dimensional...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 35 seconds ago

asked 35 seconds ago

asked 6 minutes ago

asked 14 minutes ago

asked 20 minutes ago

asked 20 minutes ago

asked 23 minutes ago

asked 26 minutes ago

asked 54 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago