I need 25,27,28

tion 175 / 871 100% + 2x1 - x2+ 3x3 - X4- 3. 25. Determine all values of the constant k for which the 16. 3x1 + 212 + 13 - 5x4--6, following system has (a) no solution, (b) an infinite number of solutions, and (c) a unique solution. x1 - 2x2 + 3x3 + X4 - 6. 2x1 + $2 - x3 + x4 = 0, X1+x2 +x3 - X4 = 4. *1 + x2+ 13 - x4= 0, 17. X1 - X2 - 13 X4 - 2, 4x1 + 2x2 - 13 + x4=0, X1 + x2 - x3 + x4 = -2, 3x1 - X2 + x3 + kx4= 0. x1 - 12 + 13 + X4 - -8. 26. Determine all values of the constants a and b for which 2x1 - x2+ 313 + 14 -X5 = 11, the following system has (a) no solution, (b) an infinite x1 - 3x2 - 2x3 - X4 - 2x5 - 2, number of solutions, and (c) a unique solution. 18. 3x1 + X2 - 2x3 - x4+ x5--2, x1 + 12 + x3= 4, x1 + 212 + x3 +12x4 + 3x5=-3, 3x1 + 5x2 - 4x3 =16, 5x1 - 3x2 - 3x3 + x4+ 2x5= 2. 2x1 + 3x2 - ax3 = b. For Problems 19-23, determine the solution set to the sys- 27. Determine all values of the constants a and b for which tem Ax = b for the given coefficient matrix A and right-hand the following system has (a) no solution, (b) an infinite side vector b. number of solutions, and (c) a unique solution. ax2 = 3, 2x1 + 12= 6, - 3x1 + (a + b)x2 = 1. 2.5 Gaussian Elimination 167 28. Show that the system 32. The system in Problem 9. x1 + x2+x3 =y1. 33. The system in Problem 13. 2x1 + 3x2 + x3 = y2, 34. (a) An n x n system of linear equations whose ma- 3x1 + 5x2+13 = 3, trix of coefficients is a lower triangular matrix is has an infinite number of solutions provided that called a lower triangular system. Assuming that ()1, y2, )3) lies on the plane with equation y1 - 2y2 + aii # 0 for each i, devise a method for solving such a system that is analogous to the back sub- y3 = 0. stitution method