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Ex 4.6, 12 - Solve system of linear equations, using matrix - Find solution of equations- Equations given

Ex 4.6, 12 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.6, 12 - Chapter 4 Class 12 Determinants - Part 3
Ex 4.6, 12 - Chapter 4 Class 12 Determinants - Part 4
Ex 4.6, 12 - Chapter 4 Class 12 Determinants - Part 5
Ex 4.6, 12 - Chapter 4 Class 12 Determinants - Part 6
Ex 4.6, 12 - Chapter 4 Class 12 Determinants - Part 7

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Ex 4.6, 12 Solve system of linear equations, using matrix method. x y + z = 4 2x + y 3z = 0 x + y + z = 2 The system of equations is x y + z = 4 2x + y 3z = 0 x + y + z = 2 Step 1 Write equation as AX = B 1 1 1 2 1 3 1 1 1 = 4 0 2 Hence A = 1 1 1 2 1 3 1 1 1 , X = & B = 4 0 2 Step 2 Calculate |A| |A| = 1 1 1 2 1 3 1 1 1 = 1 1 3 1 1 ( 1) 2 3 1 1 + 1 2 1 1 1 = ( 1 + 3) + 1 ( 2 + 3) + 1 (2 1) = 1 (4) + 1 (5) + 1 (1) = 4 + 5 + 1 = 10 Since |A| 0 The system of equation is consistent & has a unique solution Now, AX = B X = A-1 B Step 3 Calculate X = A-1 B Calculating A-1 Now, A-1 = 1 |A| adj (A) adj A = A11 A12 A13 A21 A22 A23 A31 A32 A33 = A11 A21 A31 A12 A22 A32 A13 A23 A33 A = 1 1 1 2 1 3 1 1 1 M11 = 1 3 1 1 = 1 + 3 = 4 M12 = 2 3 1 1 = 2 + 3 = 5 M13 = 2 1 1 1 = 2 1= 1 M21 = 1 1 1 1 = 1 1 = 2 M22 = 1 1 1 1 = 1 1 = 0 M23 = 1 1 1 1 = 1 + 1 = 2 M31 = 1 1 1 3 = 3 1 = 2 M32 = 1 1 2 3 = 3 4 = 5 M33 = 1 1 2 1 = 3 + 2 = 3 A11 = ( 1) 1+1 M11= ( 1)2 . 4= 4 A12 = ( 1) 1+2 M12 = ( 1) 3 . 5 = 5 A13 = ( 1) 1+3 M13= ( 1) 4 . (1) = 1 A21 = 1 2+1 M21= ( 1) 3 . (-2) = 2 A22 = ( 1) 2+2 M22 = ( 1)4 . 0 = 0 A23 = ( 1) 2+3 . M23 = ( 1) 5 . ( 2) = 2 A31 = ( 1) 3+1 . M31 = ( 1) 4 . (2) = 2 A32 = ( 1) 3+2 . M32 = ( 1) 5 . ( 5) = 5 A33 = ( 1) 3+3 . M33 = ( 1)6 . 3 = 3 Thus , adj A = 4 2 2 5 0 5 1 2 3 & |A| = 10 So, A-1 = 1 |A| adj A A-1 = 1 10 4 2 2 5 0 5 1 2 3 & B = 4 0 2 Now, solving X = A-1 B = 1 10 4 2 2 5 0 5 1 1 3 4 0 2 = 1 10 4 4 +2 0 +2(2) 0 4 +0 0 +5(2) 2 4 +1 0 +3(2) = 1 10 16+0+4 20+0+10 4+0+6 = 1 10 20 10 10 = 2 1 1 Hence, x = 2 , y = 1, & z = 1

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.