Matrices & Determinants
Properties of Determinants
Grade 12
Question:
<p>Which of the following values of \(x\) satisfy the equation<br/>\(\begin{vmatrix} (1-x)^2 & (1-2x)^2 & (1-3x)^2 \\ (2-x)^2 & (2-2x)^2 & (2-3x)^2 \\ (3-x)^2 & (3-2x)^2 & (3-3x)^2 \end{vmatrix} = -648x\)?</p>
<p>(a) -4</p>
<p>(b) 9</p>
<p>(c) -9</p>
<p>(d) 4</p>
Step-by-Step Solution
Key Concept: Factor out common expressions from rows to simplify the determinant before solving.
<p><strong>Solution:</strong> Factor out common terms from rows and columns. The determinant becomes a product of linear factors in $x$. Solve the resulting equation $\det(A) = -648x$.</p>
Correct Answer: A