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#1 2016-05-27 02:38:43

NadineSch
Member
Registered: 2016-04-24
Posts: 13

Matrix calculations - for which values does a system of equations...

Hello there. I find myself stuck with a matrix exercise:


Consider the matrices
A= ( k 3 0
       8 2  -1
      0  k  1)
and
B= (1  4  2
      2  0  -2)
k is a parameter, element of IR

b) For which value(s) of k, if any, does the matrix equation AM=A+M have a unique solution for M?
c) let k=5. Find all solutions M, if any, of the matrix equation AM=B, respectively MA=B

For a I already found a solution so I won't bother you with it.

For these two others I am lacking an idea how to even start this and google doesn't help because it is to specific I guess.

So, any advice, hint, idea and ideally showing of steps will be greatly appreciated.

Thank you,

Nadine

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#2 2016-05-27 04:45:43

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix calculations - for which values does a system of equations...

Hi;

Did you copy B right?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#3 2016-05-27 20:17:46

NadineSch
Member
Registered: 2016-04-24
Posts: 13

Re: Matrix calculations - for which values does a system of equations...

I did. Yes. And I figured it might be a hint to the solution maybe not existing with the different shape?

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#4 2016-05-27 20:23:14

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix calculations - for which values does a system of equations...

What can you multiply a 3 x 3 matrix with to get a 2 x 3?


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#5 2016-05-27 20:31:07

NadineSch
Member
Registered: 2016-04-24
Posts: 13

Re: Matrix calculations - for which values does a system of equations...

A 2 x 3?

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#6 2016-05-28 03:29:33

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix calculations - for which values does a system of equations...

Hi;

m x n . n x p = m x p

A 3 x 3 multiplied by a 2 x 3  is not legal.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#7 2016-05-28 18:42:11

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Matrix calculations - for which values does a system of equations...

Hi NadineSch,


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#8 2016-05-28 19:25:59

thickhead
Member
Registered: 2016-04-16
Posts: 1,086

Re: Matrix calculations - for which values does a system of equations...

Hi bobbym,
Did you notice "if any" in the problem statement. that fixes it. AM=B is not possible but MA=B is possible.
Hi NadineSch,


{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

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#9 2016-05-29 05:09:02

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix calculations - for which values does a system of equations...

Hi;

Please check your answer, there is a sign error, should be -6.

I had not looked at  MA = B, I was trying to get her to understand that AM = B was not possible. From the OP's comment in post #5 I thought she might be a bit confused about that.

Anyway once she understands that, MA = B can be solved without resorting to linear algebra. You need to solve the simultaneous set,

5 a + 8 b = 1,
3 a + 2 b + 5 c = 4
-b + c = 2
5 d + 8 e = 2
3 d + 2 e + 5 f = 0
-e + f = -2

This is just tedious algebraic substitutions and yields the answer.


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#10 2016-05-29 23:59:00

NadineSch
Member
Registered: 2016-04-24
Posts: 13

Re: Matrix calculations - for which values does a system of equations...

Hi there. Yes, I needed about two pages as well for the algebra. But, the good and most important news: I found the same solution!!! Jippieh!!! Thank you so much!

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#11 2016-05-30 05:54:51

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix calculations - for which values does a system of equations...

That is good.

Please memorize this formula (m x n) . (n x p) = (m x p)


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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#12 2016-07-27 23:13:24

NadineSch
Member
Registered: 2016-04-24
Posts: 13

Re: Matrix calculations - for which values does a system of equations...

For everyone that helped: I have passed my exam!! big_smile Thank you very much. I only found it polite to come back to you with this.

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#13 2016-07-28 02:04:41

zetafunc
Moderator
Registered: 2014-05-21
Posts: 2,432
Website

Re: Matrix calculations - for which values does a system of equations...

Congratulations!

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#14 2016-07-28 03:33:42

bobbym
bumpkin
From: Bumpkinland
Registered: 2009-04-12
Posts: 109,606

Re: Matrix calculations - for which values does a system of equations...

Wunderbar!


In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

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