Matrices & Determinants
Determinant Expansion and Factors
Grade 12
Question:
<p>Let $f(a,b) = \begin{vmatrix} a & a^2 & 0 \\ 1 & (2a+b) & (a+b)^2 \\ 0 & 1 & (2a+3b) \end{vmatrix}$, then which of the following is/are correct?</p>
<p>(a) $(2a+b)$ is a factor of $f(a,b)$</p>
<p>(b) $(a+2b)$ is a factor of $f(a,b)$</p>
<p>(c) $(a+b)$ is a factor of $f(a,b)$</p>
<p>(d) $a$ is a factor of $f(a,b)$</p>
Step-by-Step Solution
Key Concept: Evaluate the determinant and factor the resulting expression to identify common factors.
<p>Expand the determinant and find which expressions divide $f(a,b)$.</p>
Correct Answer: a, c