<p>If the value of a third order determinant is 11, find the value of the square of the determinant formed by the cofactors.</p>
Step-by-Step Solution
Key Concept: For an n×n determinant, the square of the determinant of cofactors equals (Δ)^(2(n-1)). For n=3, this becomes (Δ)^4.
<p><strong>Given:</strong> $n = 3$ (third order determinant) and $\Delta = 11$</p><p><strong>Using the property:</strong> For an $n \times n$ determinant, if $\Delta$ is the original determinant and $(\Delta_c)$ is the determinant of cofactors, then:</p><p>$$(\Delta_c) = (\Delta)^{n-1} = (\Delta)^2$$</p><p><strong>Therefore:</strong> $(\Delta_c)^2 = (\Delta)^{2 \cdot 2} = (\Delta)^4 = 11^4 = 14641$$</p><p>∴ The answer is 14641.</p>
Correct Answer: 14641