1.5.18 Systems of algebraic equations

Condition: Find the solution to the system of linear equations depending on the values ​​of the parameter \( \lambda \). For what values ​​of \( \lambda \) does the system allow a solution using the inverse matrix? \[ \left\{\begin{array}{c} -4 x^{1}-5 x^{2}+2 x^{3}+\lambda x^{4}=4 \lambda-1 \\ -2 x^{1}+3 x^{2}+12 x^{3}+17 x^{4}=2 \lambda-5 \\ 2 x^{1}+x^{2}+\lambda x^{3}-5 x^{4}=-4 \lambda-7 \\ 3 x^{1}+x^{2}-7 x^{3}-9 x^{4}=-3 \lambda+2 \end{array}\right. \]