worksheet03 - Worksheet#3 PHY102(Spr 2006 Matrices and...

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Worksheet #3 - PHY102 (Spr. 2006) Matrices and linear algebra Last week we did vector operations with lists . This week we introduce you to matrices, their representation using lists and to some of the matrix operations which Mathematica is able to do. Let us first see how to represent matrices in Mathematica as a list . Type “m= {{ a,b } , { c,d }} ”. Now “type MatrixForm[m]”. Note that all of the Math- ematica operations must be applied to the list form of the matrix (not the matrix form). You can see that you get the matrix m with its elements a, b, c, d in the usual form. You can think of this matrix as consisting of two row vectors (a,b) and (c,d). Type “m[[1]]” and check you get the first row vector (a,b). Now type “m[[1,1]]”; this will give you the 1st element of the first vector, namely a (notice that “m[[1]][[1]]” also does the same thing). Likewise, to access the element d , type “m[[2,2]]”. As you have done with vectors, you can perform algebraic operations on matrices. You can multiply a matrix with a vector. To see this, type “r=
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