The set of all values of λfor which the system of linear equations  2x1−2x2+x3=λx1, 2x1−3x2+2x3=λx2 ,  −x1+2x3=λx3 has a non-trivial solution

The condition for a homogeneous system of equations to have a non-trivial solution is Δ=0⇒2−λ    −2          12         −3−λ      2−1             2            −λ=0      R1→R1+R3,R2→R1+2R3⇒1−λ         0            1−λ  0             1−λ       2−2λ−1                     2                     −λ=0 ⇒1−λ21         0             10       1             2−1      2      −λ=0                    C3→C3+C1⇒1−λ21         0         00          1          2−1       2    −λ+1=0⇒1−λ2−λ+1−4=0 ⇒λ=1,−3