Determine whether the given set ?S is a subspace of the vector
space ?V.
A. ?=?2V=P2,...
Determine whether the given set ?S is a subspace of the vector
space ?V.
A. ?=?2V=P2, and ?S is the subset of ?2P2
consisting of all polynomials of the form
?(?)=?2+?.p(x)=x2+c.
B. ?=?5(?)V=C5(I), and ?S is the subset of ?V
consisting of those functions satisfying the differential equation
?(5)=0.y(5)=0.
C. ?V is the vector space of all real-valued
functions defined on the interval [?,?][a,b], and ?S is the subset
of ?V consisting of those functions satisfying
?(?)=?(?).f(a)=f(b).
D. ?=?3(?)V=C3(I), and...
Sec 6.2
1.Write an augmented matrix for the following system of
equations.
9x-8y+6z=-1
7x-5y+2z=9
6y-8z=-9
The...
Sec 6.2
1.Write an augmented matrix for the following system of
equations.
9x-8y+6z=-1
7x-5y+2z=9
6y-8z=-9
The entries in the matrix are ?
2.use row operations on the augmented matrix as far as necessary
to to determine whether they system is independent, dependent, or
inconsistent ?
4x-6y+5x=-2
-8x+12y-10z=4
-12x+18y-15z=6
3. use row operations on the augmented matrix as far as
necessary to to determine whether they system is independent,
dependent, or inconsistent ?
5x-7y+4z=13
-5x+7y-4z=-15
-10x+14y-8z=-27
4. Solve the system by...
5.
Let S be the set of all polynomials p(x) of degree ≤ 4 such
that...
5.
Let S be the set of all polynomials p(x) of degree ≤ 4 such
that
p(-1)=0.
(a) Prove that S is a subspace of the vector space of all
polynomials.
(b) Find a basis for S.
(c) What is the dimension of S?
6.
Let ? ⊆ R! be the span of ?1 = (2,1,0,-1), ?2
=(1,2,-6,1),
?3 = (1,0,2,-1) and ? ⊆ R! be the span of ?1 =(1,1,-2,0), ?2
=(3,1,2,-2). Prove that V=W.
Solve the following system of equations. (Enter your answers as
a comma-separated list. If there are...
Solve the following system of equations. (Enter your answers as
a comma-separated list. If there are infinitely many solutions,
enter a parametric solution using t and/or s. If
there is no solution, enter NONE.)
2x
−
10y
−
18z
=
35
-4x
+
20y
+
36z
=
-48
(x, y, z) = ( )
For each equation below, do the following:
- Classify the differential equation by stating its order...
For each equation below, do the following:
- Classify the differential equation by stating its order and
whether it is linear or non-linear. For linear equations, also
state whether they are homogeneous or non-homogeneous.
- Find the general solution to the equation. Give explicit
solutions only. (So all solutions should be solved for the
dependent variable y.)
a. y′ = xy2 + xy.
b. y′ + y = cos x
c. y′′′ = 2ex + 3 cos x
d. dy/dx...
1. Create a script named AnonIntegrals.m. Within it, define each
of the following functions as anonymous...
1. Create a script named AnonIntegrals.m. Within it, define each
of the following functions as anonymous functions and use the
integral command to compute its definite integral over the domain
given. Display the integral calculation to the command window. (a)
p(x) = 4x 2 − 1, x ∈ [0, 1] (b) q(x) = sin(x), x ∈ [0, π] (c) r(x)
= cos(x), x ∈ [−π/2, π/2] (d) s(x) = log(x), x ∈ [0, 1] (e) t(x) =
1 x ,...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of
the following elements:
A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x
∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J =
R.
Consider the relation ∼ on S given...
q.1.(a)
The following system of linear equations has an infinite number
of solutions
x+y−25 z=3
x−5 ...
q.1.(a)
The following system of linear equations has an infinite number
of solutions
x+y−25 z=3
x−5 y+165 z=0
4 x−14 y+465 z=3
Solve the system and find the solution in the form
x(vector)=ta(vector)+b(vector)→, where t is a free
parameter.
When you write your solution below, however, only write the part
a(vector=⎡⎣⎢ax ay az⎤⎦⎥ as a unit column vector with the
first coordinate positive. Write the results accurate to
the 3rd decimal place.
ax =
ay =
az =
Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions:...
Relations and Functions
Usual symbols for the above are;
Relations: R1, R2, S, T, etc
Functions: f, g, h, etc. But remember a function is a special
kind of relation so it might turn out that a Relation, R, is a
function, too.
Relations
To understand the symbolism better, let’s say the domain of a
relation, R, is A = { a, b , c} and the Codomain is B = {
1,2,3,4}.
Here is the relation: a R 1, ...