Check sibling questions

Ex 3.4, 16 - Find inverse of matrix [1 3 -2 -3 0 5 2 5 0]

Ex 3.4, 16 - Chapter 3 Class 12 Matrices - Part 2
Ex 3.4, 16 - Chapter 3 Class 12 Matrices - Part 3
Ex 3.4, 16 - Chapter 3 Class 12 Matrices - Part 4
Ex 3.4, 16 - Chapter 3 Class 12 Matrices - Part 5
Ex 3.4, 16 - Chapter 3 Class 12 Matrices - Part 6

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Transcript

Ex 3.4, 16 Find the inverse of each of the matrices, if it exists. [■8(1&3&−2@−3&0&−5@2&5&0)] Let A = [■8(1&3&−2@−3&0&−5@2&5&0)] A = IA [■8(1&3&−2@−3&0&−5@2&5&0)] = [■8(1&0&0@0&1&0@0&0&1)] A R2 → R2 + 3R1 [■8(1&3&−2@−𝟑+𝟑(𝟏)&0+3(3)&−5+3(−2)@2&5&0)] = [■8(1&0&0@0+3(1)&1+3(0)&0+3(0)@0&0&1)] A [■8(1&3&−2@𝟎&9&−11@2&5&0)] = [■8(1&0&0@3&1&0@0&0&1)] A R3 → R3 − 2R1 [■8(1&3&−2@0&9&−11@𝟐−𝟐(𝟏)&5−2(3)&0−2(−2))] = [■8(1&0&0@3&1&0@0−2(1)&0−2(0)&1−2(0))] A [■8(1&3&−2@0&9&−11@𝟎&−1&4)] = [■8(1&0&0@3&1&0@−2&0&1)] A R2 → 1/9 R2 [■8(1&3&−2@0/9&𝟗/𝟗&(−11)/9@0&−1&4)]= [■8(1&0&0@3/9&1/9&0/9@−2&0&1)]A [■8(1&3&−2@0&𝟏&(−11)/9@0&−1&4)] = [■8(1&0&0@1/3&1/9&0@−2&0&1)] A R3 → R3 + R2 [■8(1&3&−2@0&1&(−11)/9@0+0&−𝟏+𝟏&4+((−11)/9) )] = [■8(1&0&0@1/3&1/9&0@−2+1/3&0+1/9&1+0)] A [■8(1&3&−2@0&1&(−11)/9@0&𝟎&25/9)] = [■8(1&0&0@1/3&1/9&0@(−5)/3&1/9&1)] A R1 → R1 − 3R2 [■8(1−3(0)&𝟑−𝟑(𝟏)&−2−3((−11)/9)@0&1&(−11)/9@0&0&25/3)] =[■8(1−3(1/3)&0−3(1/9)&0−3(0)@1/3&1/9&0@(−5)/3&1/9&1)] A ` [■8(1&𝟎&5/3@0&1&(−11)/9@0&0&25/9)] = [■8(0&(−1)/3&0@1/3&1/9&0@(−5)/3&1/9&1)] A R3 → 9/25 R3 [■8(1&0&5/3@0&1&(−11)/9@0&0&𝟏)] = [■8(0&(−1)/3&0@1/3&1/9&0@(−3)/5&1/25&9/25)] A R2 → R2 + 11/9 R3 [■8(1&0&5/3@0+11/9 (0)&1+11/9(0)&(−𝟏𝟏)/𝟗+𝟏𝟏/𝟗(𝟏)@0&0&1)] =[■8(0&(−1)/3&0@1/3+11/9 ((−3)/5)&1/9+11/9 (1/25)&0+11/9 (9/25)@(−3)/5&1/25&9/25)] A [■8(1&0&5/3@0&1&𝟎@0&0&1)] = [■8(0&(−1)/3&0@(−2)/5&4/25&11/25@(−3)/5&1/25&9/25)] A R1 → R1 – 5/3 R3 [■8(1− 5/3 (0)&0− 5/3 (0)&𝟓/𝟑− 𝟓/𝟑 (𝟏)@0&1&0@0&0&1)] =[■8(0−5/3 ((−3)/5)&(−1)/3− 5/3 (1/25)&0−5/3 (9/25)@(−2)/5&4/25&11/25@(−3)/5&1/25&9/25)] A [■8(1&0&𝟎@0&1&0@0&0&1)] = [■8(5/5&(−6)/15 &(−3)/5@(−2)/5&4/25&11/25@(−3)/5&1/25&9/25)] A I = [■8(1&(−2)/5&(−3)/5@(−2)/5&4/25&11/25@(−3)/5&1/25&9/25)] A This is similar to I = A-1 A Hence, A-1 = [■8(𝟏&(−𝟐)/𝟓&(−𝟑)/𝟓@(−𝟐)/𝟓&𝟒/𝟐𝟓&𝟏𝟏/𝟐𝟓@(−𝟑)/𝟓&𝟏/𝟐𝟓&𝟗/𝟐𝟓)]

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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.