Question

Find all real values of λ, if any, for which the system has a nontrivial solution.
2x1 + 3x2 = λx1
4x1 + 3x2 = λx2

Answer 1

eigenvalues!

Answer 2

@ssf123 please stick around after you post a question so we can discuss it
the formula you have above is the same as\[A\vec x=\lambda\vec x\]the augmented matrix here being\[A=\left[\begin{matrix}2 & 3 \\ 4 & 3\end{matrix}\right]\]to find the eigenvalues we have to solve\[\det(\lambda I-A)=0\]for lambda
let me know if/where you get stuck.
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