Discussion

Which of the following is an eigen value of the matrix \(\begin{pmatrix} 3 & -1 \\ 4 & -2 \end{pmatrix}\) ?

Answer: A

An eigen value of the matrix is 2.

For the matrix with rows (3, -1) and (4, -2), the trace is 1 and the determinant is 3(-2) - (-1)(4) = -2, so the characteristic equation is

\[ \lambda^{2} - \lambda - 2 = 0 \]

\[ (\lambda - 2)(\lambda + 1) = 0 \]

The eigen values are 2 and -1. Of the options, only 2 is one of them; 0, 1 and 3 do not satisfy the equation.

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