Matrices & Determinants
Properties of determinants
Grade 12
Question:
<p>If \(\Delta\) = \[ \begin{vmatrix} a & b & c \\ d & e & f \\ g & h & i \end{vmatrix} \] and rows form G.P., then determinant is:</p>
<p>(A) 0</p>
<p>(B) \(\Delta\)</p>
<p>(C) 1</p>
<p>(D) depends</p>
Step-by-Step Solution
Key Concept: G.P. condition does not guarantee proportional rows unless ratio is same across entire rows.
1. G.P. may not ensure full row proportionality
2. Determinant depends on ratios
3. Answer = depends
Correct Answer: 4