Question

For what values of `k ,` the following system of equations possesses a nontrival solution over the set of rationals:`c+k y+3z=0,3c+k y-2z=02c+3y-4x=0.` Also find the solution for this value of `kdot`

Answer 1

Correct Answer - (k =0, the given system has infinitely many solutions)
Since, the given system of equations posses non-trivial solution, if `|{:(0, 1, -2), (0, -3, 1), (k, -5, 4):}| =0 rArr k = 0`
On solving the equation x =y =z =`lambda " " ["say"]`
`therefore `For k =0, the system has infinite solutions of `lambda in R`.