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Di¤erential Equations and Matrix Algebra I (MA 221), Fall Quarter, 1999-2000 WorkSheet 1 1) Use the Gaussian Elimination process (ie be very systematic) to solve x + 2y + z =1 2x + 6y + 5z = 6 x + 8y + 14z = 21 2) Solve and describe the solution set (if it exists) for each of the following. x + 2y = 0 x + 2y = 1 x + 2y = ¡2 x + 2y 2x + 4y = 0 2x + 4y = 2 2x + 4y = ¡4 2x + 4y =5 =2 3) Write the three systems as one augmented system and then apply Gaussian Elimination to the augmented system. Note that this augmented system will have 3 rows and 6 columns. x + 2y + 2z = 1 x + 2y + 2z = 0 x + 2y + 2z = 0 ¡y ¡ z =0 ¡y ¡ z =1 ¡y ¡ z =0 2x + z =0 2x + z =0 2x + z =1