![Ex 4.2, 10 - Chapter 4 Class 12 Determinants - Part 2](https://d1avenlh0i1xmr.cloudfront.net/839d6bfc-4570-4157-bb6c-6b487d639148/slide34.jpg)
![Ex 4.2, 10 - Chapter 4 Class 12 Determinants - Part 3](https://d1avenlh0i1xmr.cloudfront.net/c7371f2d-e376-4823-9702-8f3cb99ad903/slide35.jpg)
Making whole row/column one and simplifying
Making whole row/column one and simplifying
Last updated at April 16, 2024 by Teachoo
Question 10 By using properties of determinants, show that: (i) x+4 2x 2x 2x x+4 2x 2x 2 x+4 = (5x + 4) (4 x)2 Taking L.H.S x+4 2x 2x 2x x+4 2x 2x 2 x+4 Applying R1 R1 + R2 + R2 = x+4+2 +2 2x+x+4+2x 2x+2x+x+4 2x x+4 2x 2x 2 x+4 = + + + 2x x+4 2x 2x 2 x+4 Taking out (5x + 4) common from R1 = (5x + 4) 1 1 1 2x x+4 2x 2x 2 x+4 Applying C1 C1 C2 = (5x + 4) 1 1 1 1 2x x 4 x+4 2x 2x 2x 2 x+4 = (5x + 4) 1 1 x 4 x+4 2x 0 2 x+4 Applying C2 C2 C3 = (5x + 4) 0 1 x 4 x+4 2x 2x 0 2 4 x+4 = (5x + 4) 0 1 x 4 ( 4) 2x 0( 4) ( 4) x+4 Taking common (x 4) from C1 & C2 = (5x + 4) (x 4) (x 4) 0 0 1 1 1 2x 0 1 x+4 Expanding Determinant along R1 = (5x + 4) (x 4) (x 4) 0 1 2 1 +4 0 1 2 0 +4 +1 1 1 0 1 = (5x 4) (x 4)2 (0 0 + (1 0)) = (5x 4) (x 4)2 (1) = (5x 4) (x 4)2 = R.H.S Hence Proved