Check sibling questions

Ex 4.6, 9 - Solve using matrix method 4x-3y=3 3x+5y=7 - Ex 4.6

Ex 4.6, 9 - Chapter 4 Class 12 Determinants - Part 2
Ex 4.6, 9 - Chapter 4 Class 12 Determinants - Part 3 Ex 4.6, 9 - Chapter 4 Class 12 Determinants - Part 4


Transcript

Ex 4.6, 9 Solve system of linear equations, using matrix method. 4x – 3y = 3 3x – 5y = 7 The system of equation is 4x – 3y = 3 3x – 5y = 7 Writing equation as AX = B [■8(4&−[email protected]&−5)] [■8(𝑥@𝑦)] = [■8([email protected])] Hence A = [■8(4&−[email protected]&−5)], X = [■8(𝑥@𝑦)] & B = [■8([email protected])] Calculating |A| |A| = |■8(4&−[email protected]&−5)| = 4(–5) – 3 (–3) = –20 + 9 = – 11 Since |A| ≠ 0 ∴ System of equation is consistent & has a unique solution Now, AX = B X = A-1 B Calculating A-1 A-1 = 1/(|A|) adj (A) A = [■8(4&−[email protected]&−5)] adj A = [■8(4&−[email protected]&−5)] = [■8(−5&[email protected]−3&4)] Now, A-1 = 1/(|A|) adj A A-1 = 1/(−11) [■8(−5&[email protected]−3&4)] = 1/11 [■8(5&−[email protected]&−4)] Thus, X = A-1 B [■8(𝑥@𝑦)] = 1/11 [■8(5&−[email protected]&−4)] [■8([email protected])] [■8(𝑥@𝑦)] = 1/11 [■8(5(3)+(⤶7−3)[email protected](3)+(−4)7)] = 1/11 [■8(15−[email protected]−28)] [■8(𝑥@𝑦)] = [((−6)/11)¦((−19)/11)] Hence, x = (−𝟔)/𝟏𝟏 & y = (−𝟏𝟗)/𝟏𝟏

Davneet Singh's photo - Co-founder, Teachoo

Made by

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.