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A blow up result for a fractionally damped wave equation by Tatar N.

By Tatar N.

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Com/pic/ larsonELA6e. ΄ 2 1 0 Ϫ1 0 1 4 3 Ϫ2 ΄ Ϫ5 0 0 0 2 1 0 0 Ϫ1 3 1 0 1 (a) 0 0 1 0 (c) 0 0 ΅ ΄ 1 0 0 0 1 0 5 3 0 ΅ ΅ ΄ 0 1 0 0 0 0 1 0 Ϫ1 2 3 0 ΅ 0 (b) 0 0 3 Ϫ2 4 1 1 0 (d) 0 0 The matrices shown in parts (b) and (d) are in reduced row-echelon form. The matrices listed below are not in row-echelon form. 2 Gaussian Elimination and Gauss-Jordan Elimination 19 It can be shown that every matrix is row-equivalent to a matrix in row-echelon form. For instance, in Example 4 you could change the matrix in part (e) to row-echelon form by 1 multiplying the second row in the matrix by 2 .

X ϩ 2͒͑x Ϫ 2͒2 x ϩ 2 x Ϫ 2 ͑x Ϫ 2͒2 29. 20 I6 16 volts R1 = 4 R3 = 4 R4 = 2 8 volts Chapter 1 32. 3x2 Ϫ 7x Ϫ 12 B C A ϩ ϩ ϭ ͑x ϩ 4͒͑x Ϫ 4͒2 x ϩ 4 x Ϫ 4 ͑x Ϫ 4͒2 In Exercises 33 and 34, find the values of x, y, and ␭ that satisfy the system of equations. Such systems arise in certain problems of calculus, and ␭ is called the Lagrange multiplier. ϩ␭ ϭ0 2y ϩ ␭ ϭ0 xϩ y Ϫ4ϭ0 33. 2x 34. 2y ϩ 2␭ ϩ 2 ϭ 0 2x ␭ϩ 1ϭ0 2x ϩ y Ϫ 100 ϭ 0 35. In Super Bowl XLI on February 4, 2007, the Indianapolis Colts beat the Chicago Bears by a score of 29 to 17.

For hand computations, fractions can sometimes be avoided by judiciously choosing the order in which elementary row operations are applied. REMARK : No matter which order you use, the reduced row-echelon form will be the same. The next example demonstrates how Gauss-Jordan elimination can be used to solve a system with an infinite number of solutions. EXAMPLE 8 A System with an Infinite Number of Solutions Solve the system of linear equations. 2x1 ϩ 4x 2 Ϫ 2x3 ϭ 0 ϭ1 3x1 ϩ 5x2 SOLUTION The augmented matrix of the system of linear equations is ΄3 2 4 5 Ϫ2 0 ΅ 0 .

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