SOLUTION: III. Given the linear system 2x1 + 3x2 - x3 = 0 x1 - 4x2 + 5x3 = 0 (a) Verify that x1 = 1, x2 = -1, x3 = - 1 is a solution. (b) Verify that x1 = -2, x2 = 2, x3 = 2 is a so

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Question 1152851: III. Given the linear system
2x1 + 3x2 - x3 = 0
x1 - 4x2 + 5x3 = 0
(a) Verify that x1 = 1, x2 = -1, x3 = - 1 is a solution.
(b) Verify that x1 = -2, x2 = 2, x3 = 2 is a solution.
(c) Adding the corresponding x-values of the solution in parts (a) and (b) gives x1 = -1, x2 = 1, x3 = 1. Is this a solution to the linear system?
(d) Multiply each of the x-values in part (a) by 3. Are the resulting values a solution to the linear system?
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!




(a) Verify that , , is a solution.
......substitute given values



->
and




->
so, , , a solution

(b) Verify that , , is a solution.
......substitute given values



->
and




->
=>, , a solution
(c) Adding the corresponding x-values of the solution in parts (a) and (b) gives
, ,
Is this a solution to the linear system?
......substitute given values



->true
and




->true
=>, , a solution to the linear system

(d) Multiply each of the x-values in part (a) by 3. Are the resulting values a solution to the linear system?
, ,
......substitute given values



->
and




->
=>the resulting values solution to the linear system

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