Question

A'1(x)=2A1(x)-A2(x)-A3(x)

A'2(x)=-A1(x)+2A2(x)-A3(x)

A'3(x)=-A1(x)-A2(x)+2A3(x)

with A1(0) = 0, A2(0) = 1, and A3(0) = 5 being initial values

solve linear differential equations

Answer #1

Solved using the known method for solving linear system with real Eigen values.

Let a1 = [
7
2
-1
]
a2 =[
-1
2
3
]
a3= [
6
4
9
]
a.)determine whether a1
a2 and a3span
R3
b.) is a3 in the Span {a1,
a2}?

Events A1,A2, and A3 form a partition of sample space
S with Pr(A1)=3/7, Pr(A2)=3/7, Pr(A3)=1/7. E is an event in S with
Pr(E|A1)=3/5, Pr(E|A2)=2/5, and Pr(E|A3)=3/5.
What is Pr(E)?
What is Pr(A2|E)?
What is Pr(E')?
What is Pr(A2'|E')?

Given the augmented matrix, Find a linear combination of a1, a2,
and a3 to produce b. Verify that this produces b.
1
0
3
10
-1
8
5
6
1
-2
1
6

1. (24 pts.) For which integer values of the constant k does the
sequence {a1, a2, a3, . . .} defined by
an = (5n^k + 3)/(3n^k + 5)
converge? For those values of k, compute the limit of the
sequence {a1, a2, a3, . . .}.

1. Let |a2| = |a6| and a3=1, find an
2. 4. consecutive terms whose sum = 40
a2 * a3 = a1*a4 +8, find a1,a2,a3,a4

2. Exercise 19 section 5.4. Suppose that a1, a2, a3, …. Is a
sequence defined as follows:
a1=1 ak=2a⌊k/2⌋ for every integer k>=2.
Prove that an <= n for each integer n >=1.
plzz send with all the step

H(a1,…,an)={(x1,…,xn)∈Fn
:
a1x1+⋯+anxn=0}
Consider the special case of H(1,2,3)⊂R3
defined as above for
(a1,a2,a3)=(1,2,3)∈R3. Find a
basis for H(1,2,3) and state the dimension of
H(1,2,3).

Solve the initial value problem:
X' = (
1/2
0
1
-1/2
)X,
X(0) =
3
5

(4) Prove that, if A1, A2, ..., An are countable sets, then A1 ∪
A2 ∪ ... ∪ An is countable. (Hint: Induction.)
(6) Let F be the set of all functions from R to R. Show that |F|
> 2 ℵ0 . (Hint: Find an injective function from P(R) to F.)
(7) Let X = {1, 2, 3, 4}, Y = {5, 6, 7, 8}, T = {∅, {1}, {4},
{1, 4}, {1, 2, 3, 4}}, and S =...

Let
a1, a2, ..., an be distinct n (≥ 2) integers. Consider the
polynomial
f(x) = (x−a1)(x−a2)···(x−an)−1 in Q[x]
(1) Prove that if then f(x) = g(x)h(x)
for some g(x), h(x) ∈ Z[x],
g(ai) + h(ai) = 0 for all i = 1, 2, ..., n
(2) Prove that f(x) is irreducible over Q

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