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Instructed for all Engineers, very useful ebook on Numerical Computing with Examples in visible C++ utilizing MFC. The hyperlink of the code obtain is damaged, whereas learning eventually received it - here's the only. ftp://ftp.wiley.com/public/sci_tech_med/computing_numerical/ . get pleasure from :)

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**Sample text**

I=1 v A ∞ ∞ = max |vi | = max (|−3| , |5| , |2|) = max (3, 5, 2) = 5. 1≤i≤3 = max (|−4| + |1| + |2| , |3| + |−1| + |5| , |−2| + |−1| + |1|) = max (7, 9, 4) = 9. Row Operations Row operations are the key ingredients for reducing a given matrix into a simpler form that describes the behavior and properties of the matrix. 2. Row operation on row i with respect to row j is an operation involving addition and subtraction deﬁned as Ri ← Ri + m R j , where m is a constant and Ri denotes row i. In this deﬁnition, Ri on the left-hand side is a new value obtained from the update with Ri on the right-hand side as its old value.

Hence, a maximum total of [M+1][N+1] amount of memory is allocated to this array. Case Study: Matrix Multiplication Problem We illustrate an important tool in linear algebra involving the multiplication of two matrices whose memories are allocated dynamically. Suppose A = [aik ] and B = [bk j ] are two matrices with i = 1, 2, . . , M representing the rows of A, and j = 1, 2, . . , N are the columns in B. The basic rule allowing two matrices to be multiplied is the number of columns in the ﬁrst matrix must be equal to the number of rows of the second matrix, which is k = 1, 2, .

500 . 188 The C++ program to reduce A to U is very brief and compact. The code is constructed from the equation ai j ← ai j − m *ak j , where m = aik /akk , and i = k + 1, k + 2, . . , N , k = 1, 2, . . , N − 1 and j = 1, 2, . . cpp shows the full program for reducing A to U with Code2C. info 28 FUNDAMENTAL TOOLS FOR MATHEMATICAL COMPUTING Computing the Determinant of a Matrix As we will see later, the triangular form of a matrix says a lot about the properties of its original matrix, which includes the determinant of the matrix.