Matrices & Determinants
Properties of determinants
Grade None
Question:
<p>If \(\Delta\) = \[ \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} \] and a = d = g, then \(\Delta\) equals:</p>
<p>(A) 0</p>
<p>(B) \(\Delta\)</p>
<p>(C) 1</p>
<p>(D) depends</p>
Step-by-Step Solution
Key Concept: If two columns are identical, determinant becomes zero.
1. First column becomes (a, a, a)
2. Columns become dependent
3. Determinant = 0
Correct Answer: 1