##### 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

!! + !! !! = + !!

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