what are the eigenvalues of the 2 x 2 a-matrix: a = [a b; c d] (as calculated by hand) in matlab

To calculate the eigenvalues of a 2 x 2 matrix [a b; c d] by hand, you can use the characteristic equation:

main.m
|a - λ  b   |
|           | = 0
|c   d - λ  |
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where λ is the eigenvalue.

To solve this equation, you need to find the determinant of the matrix |a - λ b | and set it equal to zero:

main.m
det(a - λI) = 0
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where I is the identity matrix of the same size as the matrix a.

In Matlab, you can calculate the eigenvalues of a 2 x 2 matrix using the eig function. Here's an example:

main.m
a = [a b; c d];
eigenvalues = eig(a);
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The variable eigenvalues will contain the computed eigenvalues of the matrix a.

main.m

Note: Please substitute the actual values of `a`, `b`, `c`, and `d` in the above code before running it.
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