Discussion
The eigenvalues of the matrix with rows (4, 1) and (2, 3) are
Answer: A
The trace is \( 4+3=7 \) and the determinant \( (4)(3)-(1)(2)=10 \), so:
\[ \lambda^{2} - (\operatorname{tr}A)\lambda + \det A = 0 \quad\Rightarrow\quad \lambda^{2} - 7\lambda + 10 = 0 \]
\[ (\lambda-5)(\lambda-2)=0 \quad\Rightarrow\quad \lambda = 5,\; 2 \]
They duly sum to 7 and multiply to 10, which is the check.
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