Re: Linear Algebra Challenge #6
- From: pausch@xxxxxxx (Paul Schlyter)
- Date: Fri, 14 Jul 2006 07:13:22 GMT
Hey! Do your homework yourself !!!!!!!!!!!!!!!
In article <mudeb29g7muf7srsllh31nfocpl6b9hk4a@xxxxxxx>,
Rodger Rosenbaum <nospam@xxxxxxx> wrote:
Given the following matrix:
[[ 66 19 63 81 71 64 61 ]
[ 64 21 61 72 69 62 60 ]
[ 56 18 53 64 59 54 52 ]
A = [ 57 19 56 62 65 57 52 ]
[ 39 13 36 44 39 37 37 ]
[ 84 27 78 97 85 80 79 ]
[ 74 24 72 83 83 73 68 ]]
Note that it has a determinant of 1.
Find a new column vector to replace the first column, with the following
two properties:
1. With the new first column, the determinant of the matrix remains 1.
2. The Euclidean norm of the new column vector is the smallest possible.
Tell us how you did it. Try to do it using matrix and vector operations
on the HP48G or HP49G+. On the HP49G+, you should be able to get an exact
answer, but a 12 digit approximation will be acceptable.
If you must use some sort of solver and minimum finder, tell how long it
took, but remember, this is a linear algebra challenge; try to do it in a
linear algebra sort of way.
--
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Paul Schlyter, Grev Turegatan 40, SE-114 38 Stockholm, SWEDEN
e-mail: pausch at stockholm dot bostream dot se
WWW: http://stjarnhimlen.se/
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- References:
- Linear Algebra Challenge #6
- From: Rodger Rosenbaum
- Linear Algebra Challenge #6
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