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If the entries in a vector are written vertically one below the other, the vector is called a column vector. The symbol Rn denotes the set of all possible n dimensional vectors (either row vectors or column vectors). If u is an n dimensional vector with entries u1 , . . , u is contained in Rn ). An n dimensional vector is also called an n-tuple or an n-tuple vector. 14 Ch. 1. Linear eqs. In the n-dimensional vector x = (x1 , . . , xj−1 , xj , xj+1 , . . , xn ), xj is known as the j-th entry or j-th component or j-th coordinate of the vector x, for j = 1 to n.

3. Check whether this network has an Euler circuit using the algorithm discussed above. Verify the correctness of the answer by actually trying to construct an Euler circuit beginning with node 1 and explain your conclusion carefully. In this book we will discuss algorithms for solving systems of linear equations, and other related linear algebra problems. Systems of simultaneous linear equations pervade all technical areas. Knowledge about models involving simultaneous linear equations, and the fundamental concepts behind algorithms for solving and analyzing them, is extremely important for everyone with aspirations of getting any technical job.

Also, among these coins, the penny and the nickel are plain; while the dime, quarter, half dollar, dollar are reeded. The number of plain and reeded coins in the assembly has to be 194 and 250, respectively. Again, among these coins, only the quarter, half dollar, dollar have an eagle on the reverse; and the number of such coins in the assembly is required to be 209. 2 Example applications 27 this problem as a system of linear equations by ignoring the nonnegative integer requirements on the decision variables.

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