Example 10 - Show |a b c a+2x b+2y c+2z x y z| = 0 - Examples

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Example 10 Show that a﷮b﷮c﷮a+2x﷮b+2y﷮c+2z﷮x﷮y﷮z﷯﷯ = 0 Taking L.H.S a﷮b﷮c﷮a+2x﷮b+2y﷮c+2z﷮x﷮y﷮z﷯﷯ Expressing elements of 2nd row as sum of two elements = 𝐚﷮𝐛﷮𝐜﷮𝐚﷮𝐛﷮𝐜﷮x﷮y﷮z﷯﷯ + a﷮b﷮c﷮2x﷮2y﷮2z﷮x﷮y﷮z﷯﷯ = 0 + a﷮b﷮c﷮2x﷮2y﷮2z﷮x﷮y﷮z﷯﷯ = a﷮b﷮c﷮𝟐x﷮𝟐y﷮𝟐z﷮x﷮y﷮z﷯﷯ Since, all elements of 2nd row are multiplied by 2, we can take 2 outside the determinant, = 2 a﷮b﷮c﷮x﷮y﷮z﷮x﷮y﷮z﷯﷯ R2 & R3 are identical = 2 × 0 = 0 = R.H.S Thus L.H.S = R.H.S Hence proved

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