[R] How to define new matrix based on an elementary row oper

[David Winsemius]

On Aug 28, 2010, at 10:12 AM, (Ted Harding) wrote:

> On 28-Aug-10 13:15:47, Cuckovic Paik wrote:
>> Thank all help help. Ted's intuitive single step definition
>> is what I want.
>> I try to teach elementary Linear Algebra using R to manupilate
>> matrices.
>> Since my students have no programming experience at all, any fancy  
>> and
>> muliple step definition in matrix row operation will confuse them.
>> Again, I appreciate the suggestions from all of you!
>> --
>
> Just to avoid any misunderstanding: My contribution was an explanatory
> comment to Gabor's solution. It was Gabor who gave the solution!
>
> But, while I am at it, if you are teaching elementary Linear Algebra
> and matrix manipulation, note that the desired result (rows 1, 2 & 4
> of A, with row 3 = 2*(row 1 of A) + (row 3 of A)) can be obtained
> using a matrix product:
>
> 1  0  0  0  %*%   1  5  9 13
> 0  1  0  0        2  6 10 14
> 2  0  1  0        3  7 11 15
> 0  0  0  1        4  8 12 16

Which was exactly what my solution was doing, since it becomes in  
expanded form :

D2 <-  I %*% A2 + matrix (c(0,0,2,rep(0,13)), 4) %*% A2 =

1  0  0  0  %*%   1  5  9 13  +  0  0  0  0  %*%   1  5  9 13
0  1  0  0        2  6 10 14     0  0  0  0        2  6 10 14
0  0  1  0        3  7 11 15     2  0  0  0        3  7 11 15
0  0  0  1        4  8 12 16     0  0  0  0        4  8 12 16

And A %*% C + B %*% C = (A+B) %*% C and

1  0  0  0   +  0  0  0  0  =  1  0  0  0
0  1  0  0      0  0  0  0     0  1  0  0
0  0  1  0      2  0  0  0     2  0  1  0
0  0  0  1      0  0  0  0     0  0  0  1

There are other elementary operations that can be expressed as matrix  
operations:
Swapping rows 2 and 3 for instance by pre-multiplication by:

1  0  0  0
0  0  1  0
0  1  0  0
0  0  0  1

== matrix (c(1,0,0,0,0,0,1,0,0,1,0,0,0,0,0,1), 4)

Or swapping cols 2 and 3 by post multiplication with the same matrix.

-- 
David.




>
> i.e. (in R):
>
>  (diag(nrow(A)) + c(0,0,2,0, 0,0,0,0, 0,0,0,0, 0,0,0,0))%*%A
>  #      [,1] [,2] [,3] [,4]
>  # [1,]    1    5    9   13
>  # [2,]    2    6   10   14
>  # [3,]    5   17   29   41
>  # [4,]    4    8   12   16
>
> (as before).
> Ted.
>
> --------------------------------------------------------------------
> E-Mail: (Ted Harding) <Ted.Harding at manchester.ac.uk>
> Fax-to-email: +44 (0)870 094 0861
> Date: 28-Aug-10                                       Time: 15:12:03
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