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Homework Math 231. Due on the 22th May.-(Answered)

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Question

please answer the questions in the attachment, about (elementary linear algebra)?


the submission is today?


thank you


Homework
Math
231.
Due
on
the
22th
May.

 

1) Show
that
the
system
of
equations
has
infinitely
many
solutions.
Specify
exactly
the

 

solutions
and
the
limitations

(Bonus:
Graph
the
solutions)

 

! + !

 

= 3

 

!

 

!

 

!

 

2 ? +

 

= 4

 

!

 

!

 

!

 

4 + +

 

= 10

 



 

2) Use
matlab
or
any
other
software
of
your
choice
to
generate
a
10x10
random
matrix
A,

 

and
a
10x1
matrix
B.
Use
the
software
to
solve
the
system
AX=B.


 



 

3) Use
Cramer?s
rule
to
solve
the
system

 

+ + = 1

 

2 + + = 1 ? .

 

4 ? ? 2 = 1

 



 

a) Solve
the
system
when
m=1.98
and
when
m
=
2.01.
Is
there
a
big
difference

 

between
the
solutions?

 

b) Solve
the
system
when
m=4
and
m=4.03.
Is
there
a
big
difference
between
the

 

solutions?

 

c) What
can
you
conclude?

 



 

4) Relate
solving
systems
of
the
form
AX=B
to
one
of
your
previous
Engineering,
Stat
or

 

(Math
for
education
)courses.

Show
a
specific
detailed
application.
(no
computations

 

are
needed
here).

 



 

5) Given
that
the
numbers
21375,
38798,
34162,
40223
and
79154
are
all
multiples
of
19

 

prove
that
the
determinant
of
the
following
matrix
is
also
divisible
by
19.

 



 

1 2 1 3 7 5

 

1 3 8 7 9 8

 

1 3 4 1 6 2

 



 

1 4 0 2 2 3

 

1 7 9 1 5 4

 

1 0 0 0 0 19

 



 

6) Bonus


 

When
all
the
inverses
exist
prove
that





!! + !! !! = + !!

 


 

 

Paper#9256409 | Written in 27-Jul-2016

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