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Ex 3.4, 4 - Find inverse [2 3 5 7] - Class 12 CBSE - Inverse of matrix using elementary transformation

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

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Transcript

Ex3.4, 4 Find the inverse of each of the matrices, if it exists. [■8(2&3@5&7)] Let A = [■8(2&3@5&7)] We know that A = IA [■8(2&3@5&7)] = [■8(1&0@0&1)] A R1→1/2R1 [■8(𝟐/𝟐&3/2@5&7)] = [■8(1/2&0/2@0&1)] A [■8(𝟏&3/2@5" " &7" " )] = [■8(1/2&0@0&1)] A R2 →R2 – 5R1 [■8(1&3/2@𝟓−𝟓" " &7−5 (3/2)" " )] = [■8(1/2&0@0−5/2&1−5(0))] A [■8(1&3/2@𝟎" " &−1/2)] = [■8(1/2&0@(−5)/2&1)] A R2 → -2R1 [■8(1&3/2@−2(0)" " &−𝟐((−𝟏)/𝟐) )] = [■8(1/2&0@−2((−5)/2)&−2(1))] A [■8(1&3/2@0" " &𝟏)] = [■8(1/2&0@5&−2)] A R1 →R1 – 3/2 R2 [■8(1−0(3/2)&𝟑/𝟐−𝟑/𝟐(𝟏)@0" " &1)] = [■8(1/2−3/2(5)&0−3/2(−2)@5&−2)] A [■8(1&𝟎@0" " &1)] = [■8(−7&3@5&−2)] A This is similar to I = A-1A Thus, A-1 = [■8(−7&3@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.