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12 Nov 2019
Consider the system of equations below: (linear algebra)
14x - 3y + 2z + 37w = 56
21x - 5y + 3z + 56w = 81
8x - 2y + z + 21w = 30
Suppose that (a,b,c,d) and (s,t,u,v) are two particular solutions of the system, in other words, (a,b,c,d) and (s,t,u,v) represent two 4-tuples of numbers that make each of the equations true. Assume that r is any number. Show, with a complete explanation of your reasining, that (ra + (1 - r)s, rb + (1 - r)t, rc+ (1-r)u, rd + (1 - r)v) is also a solution to the system.
Consider the system of equations below: (linear algebra)
14x - 3y + 2z + 37w = 56
21x - 5y + 3z + 56w = 81
8x - 2y + z + 21w = 30
Suppose that (a,b,c,d) and (s,t,u,v) are two particular solutions of the system, in other words, (a,b,c,d) and (s,t,u,v) represent two 4-tuples of numbers that make each of the equations true. Assume that r is any number. Show, with a complete explanation of your reasining, that (ra + (1 - r)s, rb + (1 - r)t, rc+ (1-r)u, rd + (1 - r)v) is also a solution to the system.
Lelia LubowitzLv2
4 Jan 2019