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

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