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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
Question
Evaluate the determinant $\left|\begin{array}{cc}x^2-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$
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Answer

Applying $C_1\rightarrow C_1-C_2,we\ get,$

.$\left| {\begin{array}{*{20}{c}} {{x^2} - x + 1}&{x - 1} \\ {x + 1}&{x + 1} \end{array}} \right| = \left| {\begin{array}{*{20}{c}} {{x^2} - 2x + 2}&{x - 1} \\ 0&{x + 1} \end{array}} \right|$$$

$= \left( {{x^2} - 2x + 2} \right).\left( {x + 1} \right) - \left( {x - 1} \right).0$

= x3 - 2x2 + 2x + x2 - 2x + 2

= x3 - x2 + 2

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