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3 and 4 .Determinants and Matrices
easy
Evaluate the determinants : $\left|\begin{array}{cc}x^{2}-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$
A
$x^{3}+x^{2}+2$
B
$x^{3}+x^{2}-2$
C
$x^{3}-x^{2}-2$
D
$x^{3}-x^{2}+2$
Solution
$(ii)$ $\left|\begin{array}{cc}x^{2}-x+1 & x-1 \\ x+1 & x+1\end{array}\right|$
$=\left(x^{2}-x+1\right)(x+1)-(x-1)(x+1)$
$=x^{3}-x^{2}+x+x^{2}-x+1-\left(x^{2}-1\right)$
$=x^{3}+1-x^{2}+1$
$=x^{3}-x^{2}+2$
Standard 12
Mathematics