Posted by Alice on Sunday, May 17, 2009 at 5:29am.
A set of homogeneous simultaneous equations is given by
x + ky = 0
kx + 3y = 0
Calculate the two values of k that lead to nontrivial solutions to these
equations and express y in terms of x for the two values.
I thought that for the solutions to be no trivial the determinant of the coefficients had to equal zero. From this I got k=+/ sqrt 3 but I am not sure of this is right.

Math  drwls, Sunday, May 17, 2009 at 7:39am
Rewrite as
y = (1/k)x and
y = (k/3)x
There are an infinite number of solutions if the lines coincide, which happens when
1/k = k/3
k = +/sqrt3
In this case,
y = x/sqrt3 or x/sqrt3
Otherwise, there are no solutions at all, other than x=y=0. That may be what they call the "trivial" solution. Nevertheless, it is still a solution.
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