How to Divide Polynomial Matrices Using Lambda Matrices

[syj]

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. :(

 

[lanedance]

ok so do you mean
$$A(x) = \begin{pmatrix} <br /> x^3+2x^2+3 & -4x^3-x^2-5\\<br /> 3x^2-2 & x^3-2x^2+x+4 <br /> \end{pmatrix}$$

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
$$B = M\begin{pmatrix} <br /> x\\<br /> 1<br /> \end{pmatrix}$$

Then can you show, assuming x is not zero, that the inverse is
$$B^{-1} = <br /> \begin{pmatrix} <br /> \frac{1}{x} & <br /> 1<br /> \end{pmatrix}<br /> M$$

 

[syj]

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 ;)

 

[lanedance]

no worries, made a correction above, so if you were using it re-check

 

[lanedance]

ok yeah I've haven't seen lambda matricies before, this is a good intro after a google
http://solitaryroad.com/c152.html