Evaluate- begin vmatrixx- 2-x-1 - x-1 1x-1 - x-1end vmatrix

We have, x^2 x+1 amp; x 1 x+1 amp; x+1 = x^2 2x+2 amp; x 1 0 amp; x+1 [∵ C_1 → C_1 C_2] =(x^2 2x+2).(x+1) (x 1).0 =x^3 2x^2+2x+x^2 2x+2 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Determinant

Evaluate: beg...

Question

Evaluate:
$∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

Open in App

Solution

We have, $∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣ = ∣ ∣ ∣ \begin{matrix} x^{2} - 2 x + 2 & x - 1 0 & x + 1 \end{matrix} ∣ ∣ ∣$ $[∵ C_{1} \to C_{1} - C_{2}]$
$= (x^{2} - 2 x + 2) . (x + 1) - (x - 1) .0 = x^{3} - 2 x^{2} + 2 x + x^{2} - 2 x + 2 = x^{3} - x^{2} + 2$

Suggest Corrections

Similar questions

Q. Evaluate:

∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣

Q. Evaluate

∣ ∣ ∣ \begin{matrix} x & x + 1 x - 1 & x \end{matrix} ∣ ∣ ∣

Evaluate the determinant
$(i)$ $∣ ∣ ∣ \begin{matrix} cos θ & - sin θ sin θ & cos θ \end{matrix} ∣ ∣ ∣$
$(i i)$ $∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$

Q. Evaluate

∣ ∣ ∣ ∣ \begin{matrix} 1 & x & y 1 & x + y & y 1 & x & x + y \end{matrix} ∣ ∣ ∣ ∣

Q. If

f (x) = ∣ ∣ ∣ ∣ ∣ \begin{matrix} 1 & x & x + 1 2 x & x (x - 1) & x (x + 1) 3 x (x - 1) & x (x - 1) (x - 2) & x (x^{2} - 1) \end{matrix} ∣ ∣ ∣ ∣ ∣

, then f(200) is equal to

Join BYJU'S Learning Program

Evaluate: ∣∣∣x2−x+1x−1x+1x+1∣∣∣

We have, ∣∣∣x2−x+1x−1x+1x+1∣∣∣=∣∣∣x2−2x+2x−10x+1∣∣∣ [∵C1→C1−C2] =(x2−2x+2).(x+1)−(x−1).0=x3−2x2+2x+x2−2x+2=x3−x2+2

Evaluate:
$∣ ∣ ∣ \begin{matrix} x^{2} - x + 1 & x - 1 x + 1 & x + 1 \end{matrix} ∣ ∣ ∣$