TS EAMCET · Maths · Matrices
If \(P=\left|\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right|\) is the adjoint of a \(3 \times 3\) matrix \(A\) and \(\operatorname{det}(A)=4\), then \(\alpha\) is equal to
- A 22
- B 11
- C 3
- D 4
Answer & Solution
Correct Answer
(B) 11
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & |P|=\left|\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right| \\ & \Rightarrow|P|=1(12-12)-\alpha(4-6)+3(4-6) \\ & =0-(-2 \alpha)+3(-2)=2 \alpha-6\end{aligned}\) \(\because P=\operatorname{adj} A\qquad\quad\text{(given)}\)…
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