For each of the following linear systems, either solve the linear system or show that it...

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For each of the following linear systems, either solve the linear system or show that it has no solutions. Use Gaussian elimination in each case, reducing to RREF (if possible) and reading off any solutions from the matrix. (a) +2y=2, 2x+y=6, x-y+z=3 (b) 3x-2y+2=-2, -y+32=5, -x+y+2=-1 (c) 1+3=4, 21-2+2x35, 4x1-22+5x3=17 A corporation wants to lease a fleet of 8 airplanes with a combined carrying ca- pacity of 380 passengers. The three available types of planes carry 40, 50 and 60 passengers, respectively. Find how many of each type of plane could be leased by finding all non-negative integer solutions. For each of the following linear systems, either solve the linear system or show that it has no solutions. Use Gaussian elimination in each case, reducing to RREF (if possible) and reading off any solutions from the matrix. (a) +2y=2, 2x+y=6, x-y+z=3 (b) 3x-2y+2=-2, -y+32=5, -x+y+2=-1 (c) 1+3=4, 21-2+2x35, 4x1-22+5x3=17 A corporation wants to lease a fleet of 8 airplanes with a combined carrying ca- pacity of 380 passengers. The three available types of planes carry 40, 50 and 60 passengers, respectively. Find how many of each type of plane could be leased by finding all non-negative integer solutions.

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a The augmented matrix of the system is 1 2 1 2 2 1 0 6 1 1 1 3 R2 2R1 R2 R3 R1 R3 1 2 1 2 0 3 2 2 0 ... View the full answer