Home › MCQs › EEJ MAIN Mathematics › Question #6015
Back to Questions
EEJ MAIN Mathematics QUESTION #6015
Question 1

If the matrix $P = \begin{pmatrix}1 & \alpha & 3\\1 & 3 & 3\\2 & 4 & 4\end{pmatrix}$ is the adjoint of a $3\times3$ matrix $A$ with $|A|=4$, find $\alpha$.

  • 4
  • 11✔️
  • 5
Correct Answer Explanation

We use the property: $|adj(A)| = |A|^{n-1}$ for an $n\times n$ matrix. Here $n=3$, so $|P| = |A|^2 = 16$.

Compute $|P|$ by expanding along row 1 (with unknown $\alpha$):

$|P| = 1(3\cdot4-3\cdot4) - \alpha(1\cdot4-3\cdot2) + 3(1\cdot4-3\cdot2)$

$= 1(0) - \alpha(4-6) + 3(4-6) = 2\alpha - 6$

Setting $2\alpha - 6 = 16 \Rightarrow 2\alpha = 22 \Rightarrow \alpha = \mathbf{11}$