H1.pdf - MAE501 Homework#1 due Friday September 6 2019 at 11:59pm through Gradescope Problem 1(6 points It is impossible for a system of linear

# H1.pdf - MAE501 Homework#1 due Friday September 6 2019 at...

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MAE501 Homework #1 due Friday, September 6, 2019 at 11:59pm through Gradescope Problem 1 (6 points) It is impossible for a system of linear equations to have exactly two solutions. Explain why. (a) If ( x, y, z ) and ( X, Y, Z ) are two solutions, what is another one? (b) If 25 planes meet at two points, where else do they meet? Problem 2 (8 points) Find the pivots and the solution for these four equations: 2 x + y = 0 x + 2 y + z = 0 y + 2 z + t = 0 z + 2 t = 5 Problem 3 (6 points) For 4 equations with 4 unknowns u, v, w, z : True or False: to yield RREF form in the process of Gauss elimination, would the following operations be performed? (Assume no row exchanges). Note that coefficients refer to the original equations in the system, before the process of Gauss elimination started. (a) If the third equation starts with a zero coefficient (it begins with 0 u ) then no multiple of equation 1 will be subtracted from equation 3. (b) If the third equation has zero as its second coefficient (it contains 0 v ) then no multiple of equation 2 will be subtracted from equation 3.

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