Hi Everyone,
I'm new here and am using R for studying linear algebra with Lay's
Linear Algebra and Its Applications (2nd Edition). Some of the
exercises are to be solved via computer or calculator and instructions
are provided on how to use Maple, Mathematica, etc. but neither R nor
S.
So far, using R to work the problems has been straight-forward
using the matrix() and solve() functions. However, the latest set of
questions pose some difficulty:
In execises 39-42, determine if the columns of the matrix span
R4:
39) 7 2 -5 8
-5 -3 4 -9
6 10 -2 7
-7 9 2 15
(or x <- matrix(data=c(7, -5, 6, -7, 2, -3, 10, 9, -5,
4, -2, 2, 8, -9, 7, 15), nrow=4, ncol=4)
That is the whole of the question and I suppose that the way to answer
this is by determining if:
1. For each b in Rm, the equation Ax = b has a solution, or
2. A has a pivot position in every row,
where A is an (m X n) matrix.
In the Solutions Manual, there is mention of the gauss() and
bgauss() functions which apparently written by Lay - these are to
speed up matrix reduction but I have not noticed these functions in R.
So, what I'm wondering is if anyone has any ideas on how to go
about reducing this matrix in R so as to answer one of the questions
above.
Thank you very much,
Elizabeth
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