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Ex 4.6, 7 - Solve using matrix method 5x + 2y = 4, 7x + 3y = 5

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

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Transcript

Ex 4.6, 7 Solve system of linear equations, using matrix method. 5x+ 2y = 4 7x + 3y = 5 The system of equations is 5x + 2y = 4 7x + 3y = 5 Writing equation as AX = B [β– 8(5&2@7&3)] [β– 8(π‘₯@𝑦)] = [β– 8(4@5)] Hence A = [β– 8(5&2@7&3)], X = [β– 8(π‘₯@𝑦)] & B = [β– 8(4@5)] Calculating |A| |A| = |β– 8(5&2@7&3)| = 5(3) – 7(2) = 15 – 14 = 1 β‰  0 Since |A|β‰  0, System of equations is consistent & has a unique solution Now, AX = B Solution is X = A-1 B Calculating Aβˆ’1 A-1 = 1/(|A|) adj (A) A = [β– 8(5&2@7&3)] adj A = [β– 8(5&2@7&3)] = [β– 8(3&βˆ’2@βˆ’7&5)] Now, A-1 = 1/(|A|) adj A Putting values = 1/1 [β– 8(3&βˆ’2@βˆ’7&5)] = [β– 8(3&βˆ’2@βˆ’7&5)] Now X = A-1 B [β– 8(π‘₯@𝑦)] = [β– 8(3&βˆ’2@βˆ’7&5)] [β– 8(4@5)] [β– 8(π‘₯@𝑦)] = [β– 8(3(4)+(•7βˆ’2)5@βˆ’7(4)+5(5))] [β– 8(π‘₯@𝑦)] = [β– 8(2@βˆ’3)] Hence, x = 2 & y = –3

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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.