How to get eigenvalues and vectors for changing parameters in a matrix

Questions
1

Suppose I have a matrix/Stress

Tensor[{a[x],2,1},{1,2,3},{7,8,c[x]}]

both a and c are dependent on a variable x
Now I want to change x from 1-10 and find the corresponding Eigen Values and Vectors.

I tried using Range but I can’t get Eigen Vectors. It is important to know the orientation of the Eigen Values because it tells me what type of stress is being applied. Any clue on how to approach this?

2

Have you tried Eigenvalues[{{a[x], 2, 1}, {1, 2, 3}, {7, 8, c[x]}}]?

3

Do you want a Table?

Table[Eigenvalues[{{a[x], 2, 1}, {1, 2, 3}, {7, 8, c[x]}}], {x, 1, 10}]