    1. Chapter 4 Class 12 Determinants
2. Serial order wise
3. Ex 4.1

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Ex 4.1, 5 Evaluate the determinant (i) 3 1 2 0 0 1 3 5 0 3 1 2 0 0 1 3 5 0 = 3 0 1 5 0 ( 1) 0 1 3 0 +( 2) 0 0 3 5 = 3 (0(0) ( 5) ( 1) ) + 1 (0(0) 3( 1)) 2 (0( 5) 3(0)) = 3(0 5) + 1 (0 + 3) 2 (0 0) = 3( 5) + 1 (3) + 0 = 15 + 3 = 12 Ex 4.1, 5 Evaluate the determinant (ii) 3 4 5 1 1 2 2 3 1 = 3 4 5 1 1 2 2 3 1 = 3 1 2 3 1 ( 4) 1 2 2 1 + 5 1 1 2 3 = 3(1(1) 3(-2)) + 4 (1(1) (2)(-2)) + 5 (1 (3) 2 (1)) = 3 (1 + 6) + 4 (1 + 4) + 5 (3 2) = 3(7) + 4 (5) + 5(1) = 21 + 20 + 5 = 46 Ex 4.1,5 Evaluate the determinants (iii) 0 1 2 1 0 3 2 3 0 0 1 2 1 0 3 2 3 0 = 0 0 3 3 0 - 1 1 3 2 0 + 2 1 0 2 3 = 0 0 0 3 3 1 1 0 2 3 2 1 3 2 0 = 0 (0 + 9) 1 (0 6) +2 ( 3 0) = 0 1 (0 6) + 2 ( 3 0) = 1( 6) + 2 (-3) = 6 6 = 0 Ex 4.1,5 Evaluate the determinant (iv) 2 1 2 0 2 1 3 5 0 = 2 1 2 0 2 1 3 5 0 = 2 2 1 5 0 ( 1) 0 1 3 0 + ( 2) 0 2 3 5 = 2(2(0) ( 5)( 1)) +1 (0(0) 3 ( 1)) 2 (0(-5) 3 (2)) = 2(0 5) + 1 (0 + 3) 2 (0 6) = 2 ( 5) + 1(3) 2( 6) = 10 + 3 + 12 = 2 + 3 = 5

Ex 4.1 