Ex 3.2, 7 (ii) - Find X and Y, if 2X + 3Y = [] and 3X + 2Y = [] - Ex 3.2

part 2 - Ex 3.2, 7 (ii) - Ex 3.2 - Serial order wise - Chapter 3 Class 12 Matrices
part 3 - Ex 3.2, 7 (ii) - Ex 3.2 - Serial order wise - Chapter 3 Class 12 Matrices
part 4 - Ex 3.2, 7 (ii) - Ex 3.2 - Serial order wise - Chapter 3 Class 12 Matrices
part 5 - Ex 3.2, 7 (ii) - Ex 3.2 - Serial order wise - Chapter 3 Class 12 Matrices

Remove Ads

Transcript

Ex 3.2, 7 Find X and Y, if (ii) 2X + 3Y = [■8(2&3@4&0)] and 3X + 2Y = [■8(2&−2@−1&5)] Given 2X + 3Y = [■8(𝟐&𝟑@𝟒&𝟎)] Multiplying by 3 3 × (2X+ 3Y) = 3 [■8(2&3@4&0)] 6X + 9Y = [■8(2 × 3&3 × 3@4 × 3&0 × 3)] 6X + 9Y = [■8(6&9@12&0)] Given 3X + 2Y = [■8(𝟐&−𝟐@−𝟏&𝟓)] Multiplying by 2 2 × (3X + 2Y) = 2 × [■8(2&−2@−1&5)] 6X + 4Y = [■8(2 ×2&−2 ×2@−1 ×2&5 ×2)] 6X + 4Y = [■8(4&−4@−2&10)] Subtracting (1) from (2), (6X + 9Y) – (6X + 4Y) = [■8(6&9@12&0)] – [■8(4&−4@−2&10)] 6X + 9Y – 6X – 4Y = [■8(6−4&9−(−4)@12−(−2)&0−10)] 9Y – 4Y + 6X – 6X = [■8(2&9+4@12+2&−10)] 5Y + 0 = [■8(𝟐&𝟏𝟑@𝟏𝟒&−𝟏𝟎)] Y = 1/5 [■8(2&13@14&−10)] Y = [■8(𝟐/𝟓&𝟏𝟑/𝟓@𝟏𝟒/𝟓&−𝟏𝟎/𝟓)] = [■8(𝟐/𝟓&𝟏𝟑/𝟓@𝟏𝟒/𝟓&−𝟐)] Putting value of Y in (1) 6X + 9Y = [■8(6&9@12&0)] 6X + 9 [■8(2/5& 13/5@14/5&−2)] = [■8(6&9@12&0)] 6X + [■8(9 × 2/5&9 ×13/5@9 ×14/5&9 ×−2)] = [■8(6&9@12&0)] 6X + [■8(18/5&117/5@126/5&−18)] = [■8(6&9@12&0)] 6X = [■8(𝟔&𝟗@𝟏𝟐&𝟎)] – [■8(𝟏𝟖/𝟓&𝟏𝟏𝟕/𝟓@𝟏𝟐𝟔/𝟓&−𝟏𝟖)] 6X = [■8(6−18/5&9−117/5@12−126/5&0−(−18))] 6X = [■8((6 × 5 − 18)/5&(9 × 5 − 117)/5@ (12 × 5 − 126)/5&18)] 6X = [■8((30 − 18)/5&(45 − 117)/5@ (60 − 126)/5&18)] 6X = [■8(𝟏𝟐/𝟓&(−𝟕𝟐)/𝟓@ (−𝟔𝟔)/𝟓&𝟏𝟖)] X = 1/6 [■8(12/5&(−72)/5@ (−66)/5&18)] X = [■8(1/6 × 12/5&1/6 ×(−72)/5@1/6 ×(−66)/5&1/6 ×18)] X = [■8(𝟐/𝟓&(−𝟏𝟐)/𝟓@(−𝟏𝟏)/𝟓&𝟑)] Thus, X = [■8(𝟐/𝟓& (−𝟏𝟐)/𝟓@ (−𝟏𝟏)/𝟓&𝟑)] , Y = [■8(𝟐/𝟓&𝟏𝟑/𝟓@𝟏𝟒/𝟓&−𝟐)]

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 14 years. He provides courses for Maths, Science and Computer Science at Teachoo