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Edwin Fonkwe on 10 Mar 2012
Is this a homework? Did you try something?
Anyways, I can think of three ways by which you can solve the problem: (1) Use fsolve. In your case for example after having defined m, k, use: L = fsolve(@(L) det(k-L*m) initial_value); Where initial_value is a guess (which you have to make) which should be close to your expected result. Might be a bit tricky to get, but for now try 0 (zero). I don't guarantee that it will always work anyway.
(2) Use fzero. In your case for example, you first define your function: fx = @(L)det(k-L*m); answer = fzero(fx,initial_value);
Again, you have a problem here, you need to have an idea about where your solution might be found. If you don't know try different values till you think your answer is right.
(3) Personally, I prefer this third method: write your own code. Vary L in steps of, say 0.00001 and for each step, compute det(k-L*m). Evaluate the error (with respect to zero) of the result. Repeat until your result is as close as you want to zero, say it is 1e-5 for example, then stop. The value of L at that point (or previous iteration) is your answer.
Hope this helps.