TS EAMCET · Maths · Determinants
If \(\left|\begin{array}{ccc}1 & 2 & 3-\lambda \\ 0 & -1-\lambda & 2 \\ 1-\lambda & 1 & 3\end{array}\right|=\mathrm{A} \lambda^3+\mathrm{B} \lambda^2+\mathrm{C} \lambda+\mathrm{D}\), then \(\mathrm{D}+\mathrm{A}=\)
- A \(1\)
- B \(-4\)
- C \(-5\)
- D \(3\)
Answer & Solution
Correct Answer
(D) \(3\)
Step-by-step Solution
Detailed explanation
\(D = \left|\begin{array}{ccc}1 & 2 & 3 \\ 0 & -1 & 2 \\ 1 & 1 & 3\end{array}\right| = 1((-1)(3)-2(1)) - 2(0(3)-2(1)) + 3(0(1)-(-1)(1))\) \(D = 1(-3-2) - 2(0-2) + 3(0+1) = -5 + 4 + 3 = 2\) \(A\) is the coefficient of \(\lambda^3\). The only term contributing to \(\lambda^3\) is…
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