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Vectors and spaces Answers
Vectors and spaces
asked 2021-03-12
Let
\(\displaystyle{A}={b}{e}{g}\in{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}{a}&{b}\backslash{c}&{d}{e}{n}{d}{\left\lbrace{b}{m}{a}{t}{r}{i}{x}\right\rbrace}\)
and 'k' be the scalar. Find the formula that relates 'detKA' to 'K' and 'detA''
Vectors and spaces
asked 2021-03-12
Let the vector space
\(P^{2}\)
have the inner product
\(\langle p,q\rangle=\int_{-1}^{1} p(x)q(x)dx.\)
Find the following for
\(p = 1\ and\ q = x^{2}.\)
\((a) ⟨p,q⟩ (b) ∥p∥ (c) ∥q∥ (d) d(p,q)\)
Vectors and spaces
asked 2021-03-11
Find all scalars
\(c_{1} , c_{2}, c_{3}\)
such that
\(c_{1}(1 , -1, 0) + c_{2}(4, 5, 1) + c_{3}(0, 1, 5) = (3, 2, -19)\)
Vectors and spaces
asked 2021-03-08
The position vector
\(\displaystyle{r}{\left({t}\right)}={\left\langle{n}{t},\frac{{1}}{{t}^{{2}}},{t}^{{4}}\right\rangle}\)
describes the path of an object moving in space.
(a) Find the velocity vector, speed, and acceleration vector of the object.
(b) Evaluate the velocity vector and acceleration vector of the object at the given value of
\(\displaystyle{t}=\sqrt{{3}}\)
Vectors and spaces
asked 2021-03-08
A city planner wanted to place the new town library at site A. The mayor thought that it would be better at site B. What transformations were applied to the building at site A to relocate the building to site B? Did the mayor change the size or orientation of the library?
[Pic]
Vectors and spaces
asked 2021-03-02
Use
\(\displaystyle{A}{B}←→\)
and
\(\displaystyle{C}{D}←→\)
to answer the question.
\(\displaystyle{A}{B}←→\)
contains the points A(2,1) and B(3,4).
\(\displaystyle{C}{D}←→\)
contains the points C(−2,−1) and D(1,−2). Is
\(\displaystyle{A}{B}←→\)
perpendicular to
\(\displaystyle{C}{D}←→\)
? Why or why not?
Vectors and spaces
asked 2021-03-02
Let u,v1 and v2 be vectors in R^3, and let c1 and c2 be scalars. If u is orthogonal to both v1 and v2, prove that u is orthogonal to the vector c1v1+c2v2.
Vectors and spaces
asked 2021-03-02
Let U,V be subspaces of Rn. Suppose that U⊥V. Prove that {u,v} is linearly independent for any nonzero vectors u∈U,v∈V.
Vectors and spaces
asked 2021-03-01
Write an equation of the line that passes through (3, 1) and (0, 10)
Vectors and spaces
asked 2021-02-25
Let U and W be vector spaces over a field K. Let V be the set of ordered pairs (u,w) where u ∈ U and w ∈ W. Show that V is a vector space over K with addition in V and scalar multiplication on V defined by
(u,w)+(u',w')=(u+u',w+w') and k(u,w)=(ku,kw)
(This space V is called the external direct product of U and W.)
Vectors and spaces
asked 2021-02-11
What is the slope of EF if E is (0,-2) and F is (3, 2.5)
Vectors and spaces
asked 2021-02-09
Determine if
\(\displaystyle{a}.{H}={\left\lbrace\frac{{{x},{y}}}{{y}}={3}{x}-{1}\right\rbrace}\)
is a subspace of R2
\(\displaystyle{b}.{H}={\left\lbrace{a}{t}+\frac{{b}}{{b}}={8}{a}\right\rbrace}\)
is a subspace of P1
Vectors and spaces
asked 2021-02-08
m
Find m
Y=(6x+44)
Z=(-10x+65)
Vectors and spaces
asked 2021-02-08
Find the distance UV between the points U(7,−4) and V(−3,−6). Round your answer to the nearest tenth, if neces
Vectors and spaces
asked 2021-02-08
Determine the area under the standard normal curve that lies between
(a) Upper Z equals -2.03 and Upper Z equals 2.03,
(b) Upper Z equals -1.56 and Upper Z equals 0, and
(c) Upper Z equals -1.51 and Upper Z equals 0.68. (Round to four decimal places as needed.)
Vectors and spaces
asked 2021-02-06
A vector is first rotated by
\(\displaystyle{90}^{\circ}\)
along x-axis and then scaled up by 5 times is equal to
\(\displaystyle{\left({15},-{10},{20}\right)}\)
. What was the original vector
Vectors and spaces
asked 2021-02-02
Suppose the vertices of the original figure in the example were A(-6,6), B(-2,5), and C(-6,2). What would be the vertices of the image after a 90° clockwise rotation about the origin?
A'()
B'()
C'(___)
Vectors and spaces
asked 2021-01-31
Let
\(\displaystyle{B}={\left\lbrace{v}{1},{v}{2},\ldots,{v}{m}\right\rbrace}\)
be a basis for Rm. Suppose kvm is a linear combination of v1, v2, ...., vm-1 for some scalar k. What can be said about the possible value(s) of k?
Vectors and spaces
asked 2021-01-28
Given the vector
\(r(t) = { cosT, sinT, ln (CosT) }\)
and point (1, 0, 0) find vectors T, N and B at that point.
\( Vector T is the unit tangent vector, so the derivative r(t) is needed.
\( Vector N is the normal unit vector, and the equation for it uses the derivative of T(t).
\( The B vector is the binormal vector, which is a crossproduct of T and N.
Vectors and spaces
asked 2021-01-17
Let
\(\displaystyle{v}_{{1}},{v}_{{2}},\ldots.,{v}_{{k}}\)
be vectors of Rn such that
\(\displaystyle{v}={c}_{{1}}{v}_{{1}}+{c}_{{2}}{v}_{{2}}+\ldots+{c}_{{k}}{v}_{{k}}={d}_{{1}}{v}_{{1}}+{d}_{{2}}{v}_{{2}}+\ldots+{d}_{{k}}{v}_{{k}}\)
.
for some scalars
\(\displaystyle{c}_{{1}},{c}_{{2}},\ldots.,{c}_{{k}},{d}_{{1}},{d}_{{2}},\ldots.,{d}_{{k}}\)
.Prove that if
\(\displaystyle{c}{i}\ne{d}{i}{f}{\quad\text{or}\quad}{s}{o}{m}{e}{i}={1},{2},\ldots.,{k}\)
,
then
\(\displaystyle{v}_{{1}},{v}_{{2}},\ldots.,{v}_{{k}}\)
are linearly dependent.
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