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Ex 3.2, 7 - Chapter 3 Class 12 Matrices - Part 6

Ex 3.2, 7 - Chapter 3 Class 12 Matrices - Part 7
Ex 3.2, 7 - Chapter 3 Class 12 Matrices - Part 8 Ex 3.2, 7 - Chapter 3 Class 12 Matrices - Part 9 Ex 3.2, 7 - Chapter 3 Class 12 Matrices - Part 10

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

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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.