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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

  1. A 22
  2. B 11
  3. C 3
  4. D 4
Verified Solution

Answer & Solution

Correct Answer

(B) 11

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & |P|=\left|\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right| \\ & \Rightarrow|P|=1(12-12)-\alpha(4-6)+3(4-6) \\ & =0-(-2 \alpha)+3(-2)=2 \alpha-6\end{aligned}\) \(\because P=\operatorname{adj} A\qquad\quad\text{(given)}\)…