How to know if lambda is an eigenvalue of a matrix?

Find the value of x. give reasons to justify your solutions! l, m ∈ kn

Need match the functions with correct transformation. f(x) = -3x f(x) = |x-1|+3 f(x) = √(x+3) 1/2x² f(x) = (x+1)²-3 4|x| 1. compress by a factor of 1/2 2. stretch by a factor of 4 3. shift to the left 3 4. shift to the left 1 5. shift up 3 6. reflection

Mis the midpoint of rq if rm equals 2x + 5 and mq equals 4x - 9 what is the length of rq