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  4. The determinant |b2-ab&b-c&bc-ac ab-a2&a-b&b2-ab bc-ac&c-a&ab-a2| is used to

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Q. The determinant $\begin{vmatrix}b^{2}-ab&b-c&bc-ac\\ ab-a^{2}&a-b&b^{2}-ab\\ bc-ac&c-a&ab-a^{2}\end{vmatrix}$ is used to

Determinants

Solution:

Operating $C_1 \to C_1 + (a - b) C_2 - C_3$, we get
$\begin{vmatrix}b^{2}-ab&b-c&bc-ac\\ ab-a^{2}&a-b&b^{2}-ab\\ bc-ac&c-a&ab-a^{2}\end{vmatrix} $
$= \begin{vmatrix}0&b-c&bc-ac\\ 0&a-b&b^{2}-ab\\ 0&c-a&ab-a^{2}\end{vmatrix} =0$