📘 Question
Find the trace of the matrix:
\[
A =
\begin{bmatrix}
1 & -5 & 7 \\
0 & 7 & 9 \\
11 & 8 & 9
\end{bmatrix}
\]
✏️ Step-by-Step Solution
Step 1: Definition
Trace of a matrix is the sum of its diagonal elements:
\[
\text{Trace}(A) = a_{11} + a_{22} + a_{33}
\]
Step 2: Identify diagonal elements
- \(a_{11} = 1\)
- \(a_{22} = 7\)
- \(a_{33} = 9\)
Step 3: Add them
\[
\text{Trace}(A) = 1 + 7 + 9 = 17
\]
✅ Final Answer
\[
\boxed{17}
\]
💡 Key Concept
Trace is always the sum of diagonal elements of a square matrix.