How to find unknown coefficients of a given matrix

I have a matrix A with a as unknown coefficient. Need to find a. Please help! Do I use syms? Can I use root finding method?

A = [1 0 a^2; 2 0 8; 1 a 4]

B = [2; 4; 2]

[David Goodmanson]

Hi BG, what is the equation satisfied by A and B?

[BG]

𝑥1+𝑘^2 𝑥3=2

2𝑥1+8𝑥3=4

1+𝑘 𝑥2+4 x3=2

[Alan Stevens]

You have 4 unknowns and 3 equations. You need another equation (or condition, such as all solutions must be integers less than ...etc.).

Also, shouldn't the third equation be x1 + k.x2 + 4x3 = 2 ? (Not sure why you switched from a to k!).

[John D'Errico]

Why not try it?

syms a
syms x y z
A = [1 0 a^2; 2 0 8; 1 a 4];
B = [2; 4; 2];
EQ = A*[x;y;z] == B
xyz = solve(EQ,[x,y,z],'returnconditions',true)

Think about what that tells you.

[BG]

I was able to solve it using LU decomposition. Anyway, thanks for this