alleryStart learning →The TRACE of $A = \begin{pmatrix} 2 & 5 \\ 7 & 3 \end{pmatrix}$ is
A10
B12
C5
D35
Answer & Solution
Correct answer: C. 5
1. TRACE: sum of diagonal entries.
2. $\text{tr}(A) = 2 + 3 = 5$.
3. KEY FACT: trace is the SUM OF EIGENVALUES.
4. Option A would include off-diagonal entries. Option B is wrong. Option D is the determinant ($2\cdot 3 - 5 \cdot 7 = 6 - 35 = -29$, actually neither).
_Source: Sergei Treil, "Linear Algebra Done Wrong", §4.6 (Trace)._
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