12 Solving Systems of Equations by Elimination (i) (a) x + 2y = 4 (ii) (a) (b) 3x+y= 9 (c) x-3y = 1 (iii) (a) 2x + y - 2z = -5 xy+ z = 189 23 x + y z=> = -3 (b) (c) -2x+4y-4z = (b) 3x - y + z = 8 2z = .5 (c) 6x+.5y 3. Solve the following systems of equations using Gaussian elimination. (a) 2x-3x2 + 2x3 = 0 = 7 -x, +5x2 + 4x3 = 4 - 2 (b) -x x2 + x3 = 2x + 2x2 - 4x3 = -4 x1 - 2x2 + 3x3 = = 5 (c) -r. - 3r 1. and programs, by the proper "program of such computations is having the right be it a matrix decomposition or some other transformed form of the matrix. ces is the preprocessing, to get the right representation of the data. The key stage in virtually all modern numerical algorithms involving matri Section 3.2 Exercises Summary of Exercises Exercises 1-16 involve Gaussian elimination computations. Exercises 17-20 involve word problems. Exercises 21-25 are theoretical. 1. Solve the following systems of equations by Gaussian elimination. (a)x + y = 5 x-2y=4 - (b) 2x 3y=4 3x + 2y = 5 (c) 3x-y=0 - 2x + y = 2 2. In each of the following sets of three equations, show that the third equation equals the second equation minus some multiple of the first equation: (c)(b) - r(a) for some r.