Given the equation: ( 2 , − 14 , 8 ) x + ( −...

on2t1inf8b

on2t1inf8b

Answered

2022-07-21

Given the equation:
( 2 , 14 , 8 ) x + ( 3 , 21 , 12 ) y = 0
Find the scalars x and y, not both zero, such that the above equation holds.
My attempt:
I tried solving the equation system 2x−3y=0,−14x+21y=0,8x−12y=0 but I only obtained trivial solutions, i.e. x=0,y=0

Answer & Explanation

Bradley Sherman

Bradley Sherman

Expert

2022-07-22Added 17 answers

Your effort makes a lot of sense! But you not only find the trivial solution: your system of equations is correct and it is equivalent to the only equation:
2 x 3 y = 0 ,
whose solution is
y = 2 3 x .
So, all the ordered couples of the kind ( x , y ) = ( x , 2 3 x ) are solutions.
The trivial solution (0,0) is an example, other ones are ( 1 , 2 3 ) and (3,2) or (−3,−2) but one linear equation in two variables has an infinity of such ordered couples of values as solutions.

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