# Ex 3.4, 17 - Chapter 3 Class 12 Matrices (Term 1)

Last updated at Jan. 17, 2020 by

Last updated at Jan. 17, 2020 by

Transcript

Ex3.4, 17 Find the inverse of each of the matrices, if it exists. [■8(2&0&−1@5&1&0@0&1&3)] Let A =[■8(2&0&−1@5&1&0@0&1&3)] We know that A = IA [■8(2&0&−1@5&1&0@0&1&3)]= [■8(1&0&0@0&1&0@0&0&1)] A R1 →1/2 R1 , [■8(𝟐/𝟐&0/2&(−1)/2@5&1&0@0&1&3)]= [■8(1/2&0/2&0/2@0&1&0@0&0&1)] A [■8(𝟏&0&−1/2@5&1&0@0&1&3)] = [■8(1/2&0&0@0&1&0@0&0&1)] A R2 → R2 – 5R1 [■8(1&0&−1/2@𝟓−𝟓(𝟏)&1−5(0)&0−5((−1)/2)@0&1&3)] = [■8(1/2&0&0@0−5(1/2)&1−5(0)&0−5(0)@0&0&1)] A [■8(1&0&−1/2@𝟎&1&5/2@0&0&3)]= [■8(1/2&0&0@−5/2&1&0@0&0&1)] A R3 → R3 – R2 [■8(1&0&−1/2@0&1&5/2@𝟎&0&3−5/2)]= [■8(1/2&0&0@−5/2&1&0@0−(−5/2)&0−1&1−0)] A [■8(1&0&−1/2@0&1&5/2@𝟎&0&1/2)]= [■8(1/2&0&0@−5/2&1&0@5/2&−1&1)] A R3 → 2R3 [■8(1&0&−1/2@0&1&5/2@2 × 0&2 × 0&𝟐 × 𝟏/𝟐)] = [■8(1/2&0&0@−5/2&1&0@2 × 5/2&2 × (−1)&2 × 1)] A [■8(1&0&−1/2@0&1&5/2@0&0&𝟏)]= [■8(1/2&0&0@−5/2&1&0@5&−2&2)] A R1 → R1 + 1/2 R3 [■8(1+1/2(0)&0+1/2(0)&(−𝟏)/𝟐+𝟏/𝟐(𝟏)@0&1&5/2@0&0&1)]= [■8(1/2+1/2(5)&0+1/2(−2)&0+1/2(2)@(−5)/2&1&0@5&−2&2)] A [■8(1&0&𝟎@0&1&5/2@0&0&1)]= [■8(3&−1&1@(−5)/2&1&0@5&−2&2)] A R2 → R2 − 5/2 R3 [■8(1&0&0@0−5/2(0)&1−5/2(0)&𝟓/𝟐−𝟓/𝟐(𝟏)@0&0&1)] = [■8(3&−1&1@(−5)/2−5/2 (5)&1−5/2 (−2)&0−5/2@5&−2&2) (2)] A [■8(1&0&0@0&1&𝟎@0&0&1)]= [■8(3&−1&1@(−30)/2&6&−5@5&−2&2)] A "I" = [■8(3&−1&1@−15&6&−5@5&−2&2)] A This is similar to I = A-1A Thus, A-1 = [■8(𝟑&−𝟏&𝟏@−𝟏𝟓&𝟔&−𝟓@𝟓&−𝟐&𝟐)]

Ex 3.4

Ex 3.4, 1
Deleted for CBSE Board 2022 Exams

Ex 3.4, 2 Deleted for CBSE Board 2022 Exams

Ex 3.4, 3 Deleted for CBSE Board 2022 Exams

Ex 3.4, 4 Deleted for CBSE Board 2022 Exams

Ex 3.4, 5 Deleted for CBSE Board 2022 Exams

Ex 3.4, 6 Deleted for CBSE Board 2022 Exams

Ex 3.4, 7 Deleted for CBSE Board 2022 Exams

Ex 3.4, 8 Important Deleted for CBSE Board 2022 Exams

Ex 3.4, 9 Deleted for CBSE Board 2022 Exams

Ex 3.4, 10 Deleted for CBSE Board 2022 Exams

Ex 3.4, 11 Deleted for CBSE Board 2022 Exams

Ex 3.4, 12 Deleted for CBSE Board 2022 Exams

Ex 3.4, 13 Deleted for CBSE Board 2022 Exams

Ex 3.4, 14 Deleted for CBSE Board 2022 Exams

Ex 3.4, 15 Important Deleted for CBSE Board 2022 Exams

Ex 3.4, 16 Deleted for CBSE Board 2022 Exams

Ex 3.4, 17 Important Deleted for CBSE Board 2022 Exams You are here

Ex 3.4, 18 (MCQ) Deleted for CBSE Board 2022 Exams

Chapter 3 Class 12 Matrices (Term 1)

Serial order wise

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.