WI08ma1bMathematica3

# - Math 1b practical Mathematica Session 3(Are these"sessions of any value At In[1 we teach Mathematica how to produce"random m by n matrices At

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Math 1b practical January 28, 2009 Mathematica Session 3 (Are these "sessions" of any value?) At In[1], we teach Mathematica how to produce "random" m by n matrices. At In[2], we teach Mathematica an abbreviation for MatrixForm. At In[3], we construct a 5 by 8 matrix A, which we know will have rank at most 3, because its rows are linear combinations of a 3 by 8 matrix. Row reduction produces a basis for the row space of A, namely the three nonzero rows of Out[4]. There are many bases for the row space of A and we remark that Mathematica can do "LatticeReduce" which implemements what is known as the "LLL algorithm" to find a basis for the row space of an integer matrix that consists of relatively simple integer vectors. Just for fun, we tried it on A and got the rows of Out[5]. The echelon form of the transpose of A is shown at Out[7]. We see the rows of A are linearly dependent; e.g. the fourth and fifth rows of A (columns of the transpose of A) are linear combinations of the first three rows.

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## This note was uploaded on 09/25/2010 for the course MATH 1bPRAC taught by Professor Wilson during the Winter '09 term at Caltech.

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- Math 1b practical Mathematica Session 3(Are these"sessions of any value At In[1 we teach Mathematica how to produce"random m by n matrices At

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