JEE Mains · Maths · STD 12 - 3 and 4 . metrices and determinant
If \(B = \left[ {\begin{array}{*{20}{c}}
5&{2\alpha }&1\\
0&2&1\\
\alpha &3&{ - 1}
\end{array}} \right]\) is the inverse of a \(3 \times 3\) matrix \(A\), then the sum of all values of \(\alpha \) for which \(det\, (A) + 1 = 0\), is
- A \(0\)
- B \(-1\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(\left| B \right| = 5\left( { - 5} \right) - 2\alpha \left( { - \alpha } \right) - 2\alpha \) \( = 2{\alpha ^2} - 2\alpha - 25\) \(1 + \left| A \right| = 0\) \({\alpha ^2} - \alpha - 12 = 0\) Sum \(=1\)
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