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hilbert = HilbertMatrix[6]; hilbert // MatrixForm 1 1 2 1 3 1 4 1 5 1 6 1 2 1 3 1 4 1 5 1 6 1 7 1 3 1 4 1 5 1 6 1 7 1 8 1 4 1 5 1 6 1 7 1 8 1 9 1 5 1 6 1 7 1 8 1 9 1 10 1 6 1 7 1 8 1 9 1 10 1 11

Once you set up the wireless sync, your Google Contacts and Calendar information will flow quickly into your iPad. Note that if you have thousands of contacts, it could take several minutes for the first sync to complete. You may want to go back and review 13 Contacts and 14 Calendar for details about working with both apps.

Det[hilbert] 1 186 313 420 339 200 000

Fig. 2-5.

MatrixForm[Inverse[hilbert], TableAlignments Right]

NOTE: Since the sync with Google or Exchange is wireless, you ll need to make sure you have an active network connection from your iPad. Check out 4, Wi-Fi and 3G Connectivity, to learn more.

36 630 3 360 7 560 7 560 -2 772 630 14 700 -88 200 211 680 220 500 83 160 564 480 1 411 200 1 512 000 0 582 120 3 360 88 200 7 560 211 680 1 411 200 1 3 628 800 3 969 000 1 552 320 1 512 000 3 969 000 4 410 000 1 746 360 7 560 220 500 2 772 83 160 582 120 1 552 320 1 746 360 0 698 544

TableForm[Table[{k, Det[HilbertMatrix[k]] // N}, {k, 1, 10}], TableSpacing {1, 5}, TableHeadings {None, {"k", "determinant"}}]

Working with Multiple Address Books (Groups)

k 1 2 3 4 5 6 7 8 9 10 determinant 1. 0.0833333 0.000462963 1.65344 10 7 3.7493 10 12 5.3673 10 18 4.8358 10 25 2.73705 10 33 9.72023 10 43 2.16418 10 53 Since the determinants are nonzero, each Hilbert matrix is invertible. The Hilbert matrix is a classic example of an ill-conditioned matrix.

In object-oriented development ( 11), both the problem in the problem domain and the solution in the machine space are described in terms of objects In the solution, these objects normally become classes As the requirements and design phases of software development progress, the objects switch from being representations of the things in the problem domain to being programming structures in the software Object models represent entities and relationships between entities Each box represents a type of object, and the name, attributes, and the methods of the object are listed inside the box The top section of the box is for the name of the object, the second section is for the attributes, and the bottom section is for the methods An arc between two objects represents a relationship between the objects Arcs may be labeled in the center with a name of the association.

2 10 3 10 4 10

If you ve added some contacts to your iPad or synced it at least once with iTunes, you may end up with two groups of contacts, as shown in Figure 24-1.

1 2 7 m = 1 3 3 4 ; 10 5 4 1 Limit[MatrixPower[m, n], n // MatrixForm 47 150 47 150 47 150 23 19 75 50 23 19 75 50 23 19 75 50

1 2 1 2 3 1 2 2 0 2 0 1 2 3 1 and f ( x ) = x 5 + 2 x 4 x 3 + x 2 3 x + 2. Compute f(A). 12.15 Let A = 1 1 1 2 3 1 1 2 2 2