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SOLUTION QRCode Scanner In None Using Barcode Control SDK for Software Control to generate, create, read, scan barcode image in Software applications. Creating QR Code ISO/IEC18004 In None Using Barcode encoder for Software Control to generate, create QR Code image in Software applications. Combinatorica` letters={a, b, c, d, e}; KSubsets[letters, 3] QR Code JIS X 0510 Scanner In None Using Barcode scanner for Software Control to read, scan read, scan image in Software applications. Encoding QRCode In C# Using Barcode printer for .NET Control to generate, create QR image in VS .NET applications. {{a, b, c}, {a, b, d}, {a, b, e}, {a, c, d}, {a, c, e}, {a, d, e}, {b, c, d}, {b, c, e}, {b, Encode QRCode In .NET Framework Using Barcode encoder for ASP.NET Control to generate, create QR Code 2d barcode image in ASP.NET applications. QR Code Encoder In VS .NET Using Barcode maker for .NET Control to generate, create Quick Response Code image in .NET applications. d, e}, {c, d, e}} QR Code 2d Barcode Creator In VB.NET Using Barcode generator for Visual Studio .NET Control to generate, create QR Code 2d barcode image in .NET framework applications. Drawing Bar Code In None Using Barcode maker for Software Control to generate, create barcode image in Software applications. Length[%] 10 Code 128B Encoder In None Using Barcode creator for Software Control to generate, create Code 128A image in Software applications. Code39 Maker In None Using Barcode generator for Software Control to generate, create Code 3 of 9 image in Software applications. 3.5 Tables and Matrices
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TableForm[list] or list //TableForm 1 2 3 4 5 6 7 8 9 10 11 12
Matrices and tables can also be conveniently entered by going to Insert Table/Matrix New.
Clicking OK yields an empty grid use the [TAB] key to cycle from entry to entry.
EXAMPLE 43
list = {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}}; {{1, 2, 3, 4}, {5, 6, 7, 8}, {9, 10, 11, 12}} or list //MatrixForm
MatrixForm[list] 1 2 3 4 5 6 7 8 9 10 11 12 Two special matrixgenerating commands are worth remembering because of their frequency in applications. These generate a nested list. Use MatrixForm to get a matrix. IdentityMatrix[n] produces an n n matrix with 1s on the main diagonal and 0s elsewhere. DiagonalMatrix[list] creates a diagonal matrix whose diagonal entries are the elements of list. Lists
EXAMPLE 44
IdentityMatrix[3] //MatrixForm 1 0 0 0 1 0 0 0 1 DiagonalMatrix[{1, 2, 3}] //MatrixForm 1 0 0 0 2 0 0 0 3 Once defined, matrices can be combined using the operations of addition, subtraction, scalar, and matrix multiplication. The operation of matrix multiplication is represented by a period (.). Matrices are discussed in greater detail in 12. EXAMPLE 45
1 2 3 A = 4 5 6 7 8 9 {{1, The matrix is input using Insert Table/Matrix New. Mathematica outputs the matrix as a nested list of numbers. 2, 3},{4, 5, 6},{7, 8, 9}} 2 1 5 B = 4 7 2 1 3 2 {{2, 1, 5},{4, 7, 2},{1, 3, 2}} A + B //MatrixForm 3 3 8 8 12 8 8 11 11 A B //MatrixForm 1 1 2 0 2 4 6 5 7 3 A //MatrixForm 3 6 9 12 15 18 21 24 27 A.B //MatrixForm 13 24 15 34 57 42 55 90 69 It is useful to remember that if list is a simple list of numbers, list.list yields the sum of their squares. The result is printed as a single number without braces. EXAMPLE 46
list = {1, 2, 3, 4, 5}; list.list 55
Lists
Tables are also stored as nested lists, but are represented as tables with TableForm. Although this command allows representation of tables of any dimension, we will discuss only one and twodimensional tables in this book. EXAMPLE 47
list = {{12, 7, 10}, {105, 205, 7}, {3, 30, 300}}; list//TableForm
12 105 3 7 205 30 10 7 300 TableForm[list, options] allows the use of various formatting options in determining the appearance of a table. From Example 47 we can observe that the numbers in a table are, by default, left justified. This can sometimes make the table confusing to read. Justification can be controlled with the TableAlignments option. TableAlignments Left justifies the columns to the left (default). TableAlignments Right justifies the columns to the right. TableAlignments Center centers the columns. EXAMPLE 48
list = {{12,7,10},{105,205,7},{3,30,300}}; TableForm[list, TableAlignments Right] 12 7 10 105 205 7 3 30 300 TableForm[list, TableAlignments Center] 12 105 3 7 205 30 10 7 300 Row and column headings can be inserted by using the option TableHeadings within the TableForm command. The default is TableHeadings None. TableHeadings Automatic produces consecutive integer labels for both rows and columns. Each row and column of a table can be labeled separately using strings (characters enclosed within double quotes) or Mathematica expressions. The general form of this option is TableHeadings {rowlist, columnlist} where rowlist is a list of row labels and columnlist is a list of column labels. If you desire to have row labels but not column labels, or column labels but not row labels, simply replace rowlist or columnlist by None.

