+0  
 
0
41
1
avatar

Find all values of k for which the system

x + ky - z = 0

kx - y - z = 0

7x + 3y - 2kz = 0

has a non-trivial solution.  (In other words, find all values of k for which the system has a solution other than (x,y,z) = (0,0,0).)

 May 14, 2022
 #1
avatar+9457 
0

For a homogeneous system \(A \vec x = \vec 0\) to have non-trivial solutions, we must have \(\det A = 0\).

 

Then \(\det \begin{pmatrix}1&k&-1\\k&-1&-1\\7&3&-2k\end{pmatrix}= 0\). Please simplify the determinant and solve the resulting cubic equation.

 May 14, 2022
edited by MaxWong  May 14, 2022

13 Online Users

avatar