Q : 2      

(ii)        \begin{vmatrix}x^2-x+1 & x-1\\x+1 &x+1 \end{vmatrix}

Answers (1)

We have determinant \begin{vmatrix}x^2-x+1 & x-1\\x+1 &x+1 \end{vmatrix}

So, \dpi{100} \begin{vmatrix}x^2-x+1 & x-1\\x+1 &x+1 \end{vmatrix} = (x^2-x+1)(x+1) - (x-1)(x+1)

= (x+1)(x^2-x+1-x+1) = (x+1)(x^2-2x+2)

=x^3-2x^2+2x +x^2-2x+2

= x^3-x^2+2

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