Applied Linear Algebra Exam 3 Questions And Answers Latest Update.docx

Applied Linear Algebra Exam 3 Questions
And Answers Latest Update
The set of all polynomials of the form
p(t)=at6,
where a is in
ℝ. - - -
correct answer ✅The set is a subspace of
ℙ6.
The set contains the zero vector of
ℙ6,
the set is closed under vector addition, and the set is closed under
multiplication by scalars.


Let
v1=10−1,
v2=213,
v3=921,
and
w=318.
Is w in the subspace spanned by
{v1,
v2,

,Applied Linear Algebra Exam 3 Questions
And Answers Latest Update
v3}?
Why? - - -
correct answer ✅Vector w is not in the subspace spanned by
{v1,
v2,
v3}
because the equation
x1v1+x2v2+x3v3=w
has no solution which can be seen because an echelon form of the
augmented matrix of the system has a row of the form [0
•••
0 b] with
b≠0.


The set
M2×2
of all
2×2

, Applied Linear Algebra Exam 3 Questions
And Answers Latest Update
matrices is a vector space, under the usual operations of addition of
matrices and multiplication by real scalars. Determine if the set H of
all matrices of the form
ab0d


is a subspace of
M2×2. - - -
correct answer ✅


Determine whether the statement is True or False. Justify your
answer.
ℝ2
is a subspace of ℝ3. - - -
correct answer ✅


Either use an appropriate theorem to show that the given set, W, is
a vector space, or find a specific example to the contrary.
W=rst : 2r−3=s+5t
The set W is a subset of ℝ3. If W were a vector space, what else
would be true about it? - - -
correct answer ✅The set W would be a subspace of