Matrices & Determinants
Determinant Algebra
Grade 12
Question:
<p>Let \(f(a,b) = \begin{vmatrix} a & a^2 & 0 \\ 1 & 2a + b & (a+b)^2 \\ 0 & 1 & 2a + 3b \end{vmatrix}\). Which is a factor of \(f(a,b)\)?</p>
<p>(a) \((a + b)\)</p>
<p>(b) \((a + 2b)\)</p>
<p>(c) \((2a + b)\)</p>
<p>(d) \(a\)</p>
Step-by-Step Solution
Key Concept: Systematically expand the determinant and factor the resulting polynomial expression.
<p>Expand the determinant using cofactor expansion. Factor out common terms to identify $(a+b)$ as a factor.</p>
Correct Answer: A