Question

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 |

Answer #1

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

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')?

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

1) Suppose a1, a2, a3, ... is a sequence of integers such that
a1 =1/16 and an = 4an−1. Guess a formula for an and prove that your
guess is correct.
2) Show that given 5 integer numbers, you can always find two of
the numbers whose difference will be a multiple of 4.
3) Four cats and five mice form a row. In how many ways can they
form the row if the mice are always together?
Please help...

Given that A1 = B1 minus B2,
A2 = B2 minus B3, and
A3 = B3 minus B1, Find the joint
p.m.f. (probability mass function) of A1 and
A2, where Ai ~ Ber(p) for all random
variables i in {1,2,3}

Given that A1 = B1 minus
B2,A2 =
B2 minus B3, and
A3 = B3 minus
B1, Find the joint p.m.f.
(probability mass function) of A1 and A2,
where Bi ~ Ber(p) for all
random variables i in {1,2,3}

Please give examples of matrices which
(1) is an augmented matrix of a linear system which 3 equations
and 3 variables.
(2) is an augmented matrix of a linear system which 3 equations
and 3 variables and all variables should be presented.
(3) is an augmented matrix of a linear system which 3 equations
and 3 variables and one of the variables is not presented.
(4) is an augmented matrix of a linear system which is
inconsistent. (5) is an...

(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 =...

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).

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