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Dividing polynomial matrices

  • Thread starter syj
  • Start date
  • #1
syj
55
0

Homework Statement



Divide

A(x)=
[x3+2x2+3 -4x3-x2-5]

[3x2-2 x3-2x2+x+4]

by

B(x) =
[x+4 -3]
[-x+6 x+2]

on both the right side and the left side.


Homework Equations





The Attempt at a Solution



I am thinking i need to rewrite A(x) as:

[1 -4]
[0 1 ] x3 +


[2 -1]
[3 -2]x2+

[0 0]
[0 1]x +

[3 -5]
[-2 4]
and do the same to B(x)

but i don't know what to do from there. :(
 

Answers and Replies

  • #2
lanedance
Homework Helper
3,304
2
ok so do you mean
[tex] A(x) = \begin{pmatrix}
x^3+2x^2+3 & -4x^3-x^2-5\\
3x^2-2 & x^3-2x^2+x+4
\end{pmatrix}
[/tex]

i have to admit I don't really understand the question. What do you mean by divide? The matrix equivalent would be to multiply by the inverse, assuming it exists

It me help to write B as
[tex]
B = M\begin{pmatrix}
x\\
1
\end{pmatrix}
[/tex]

Then can you show, assuming x is not zero, that the inverse is
[tex]
B^{-1} =
\begin{pmatrix}
\frac{1}{x} &
1
\end{pmatrix}
M
[/tex]
 
Last edited:
  • #3
syj
55
0
thanks
i found a book online that explained the method.
except in the book they referred to the matrix as a lambda matrix not a polynomial matrix.
thanks again for all the help.
i shall be posting more questions soon ;)
 
  • #4
lanedance
Homework Helper
3,304
2
no worries, made a correction above, so if you were using it re-check
 
  • #5
lanedance
Homework Helper
3,304
2
ok yeah I've haven't seen lambda matricies before, this is a good intro after a google
http://solitaryroad.com/c152.html
 

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