There is no "k" in your equations. I assume you're looking for values of lambda, not "k", right?
Can you set this up as a matrix? Can you row-reduce that matrix?
Using either Gaussian or Gauss-Jordan elimination, find the value(s) of k, if any, for which the following system will have
(i) no solution
(ii) a unique solution, and
(iii) infinitely many solutions
x − 3z = −3
−2x − λy + z = 2
x + 2y + λz = 1
Thanks for any help
I took the determinant of
to get Det(A) = and i used the quadratic formula to get the roots, . A system has zero or infinitely many solution only when Det(A) = 0. so Det(A) = 0, when . I then found that for using row reducing, that the system didint have a solution, and again for , i found out by row reducing that it had infinite soln.