Question: 1. Solve the following set of equations using matrix methods.
x1 + 2x2 + 2x3 = 1
2x1 + 2x2 + 3x3 = 3
x1 - x2 + 3x3 = 5
2. Determine those values of λ for which the following set of equations may possess a nontrivial solution.
3x1 + x2 - λx3 = 0
4x1 - 2x2 - 3x3 = 0
2λx1 + 4x2 + λx3 = 0
For each permissible value of λ, determine the most general solution.