Ex 4.2, 5 - Chapter 4 Class 12 Determinants

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Ex 4.2, 5 Using the property of determinants and without expanding, prove that: b+c q+r y+z c+a r+p z+x a+b p+q x+y = 2 a p x b q y c r z Taking L.H.S b+c q+r y+z c+a r+p z+x a+b p+q x+y Applying R3 R3 + R2 + R1 = b+ + + c+a r+ z+x a+b+c+a+b+c + + + + + x+ + + + + = b+ + + c+a r+ z+x (a+b+c) ( + + ) (x+ + ) Taking 2 common from R3 = 2 b+ + + c+a r+ z+x (a+b+c) ( + + ) (x+ + ) Applying R1 R1 R3 = 2 b+ + + c+a r+ z+x a+b+c + + x+ + = 2 c+a r+ z+x a+b+c + + x+ + Applying R2 R2 R3 = 2 c+a a b c r+ z+x x y z a+b+c + + x+ + = 2 b y a+b+c + + x+ + Applying R3 R3 + R1 + R2 = 2 b y a+b+c + + x+ + = 2 b y Taking 1 Common from R1 & R3 = 2 ( 1) ( 1) b y = 2 b y = R.H.S Hence Proved