# Misc 7 - Chapter 4 Class 12 Determinants

Last updated at Jan. 23, 2020 by Teachoo

Last updated at Jan. 23, 2020 by Teachoo

Transcript

Misc 7 If A-1 = [■8(3&−1&1@−15&6&−5@5&−2&2)] and B = [■8(1&2&−2@−1&3&0@0&−2&1)] , Find (AB)-1 We know that (AB)−1 = B−1 A−1 We are given A-1 , so calculating B−1 Calculating B−1 We know that B−1 = 1/(|B|) adj (B) exists if |B| ≠ 0 |B| = |■8(1&2&−2@−1&3&0@0&−2&1)| = 1 (3 – 0) – 2(– 1 – 0) –2 (2 – 0) = 1 (3) –2 (–1) –2(2) = 3 + 2 – 4 = 1 Since |B| ≠ 0 Thus, B-1 exists Calculating adj B Now, adj B = [■8(A_11&A_21&A_31@A_12&A_22&A_32@A_13&A_23&A_33 )] B = [■8(1&2&−2@−1&3&0@0&−2&1)] M11 = |■8(3&0@−2&1)| =3(1) – (–2)0 = 3 M12 = |■8(−1&0@0&1)| = -1(1) – 0(0)= –1 M13 = |■8(−1&3@0&−2)| =(–1)(–2) – 0(3)= 2 M21 = |■8(2&−2@−2&1)| =2(1)–(–2)(–2)= –2 M22 = |■8(1&−2@0&1)| = 1(1) – 0(−2) = 1 M23 = |■8(1&2@0&−2)| = 1(-2) – 0(2) = –2 M31 = |■8(2&−2@3&0)| = 2(0) – 3(−2) = 6 M32 = |■8(1&−2@−1&0)| =1(0)–(–1)(–2)= –2 M33 = |■8(1&2@−1&3)| = 1(3) – (–1)2 = 5 Now, A11 = (–1)1+1 M11 = (–1)2 . 3 = 3 A12 = (–1)1+2 M12 = (–1)3 (–1) = 1 A13 = (–1)1+3 M13 = (–1)4 2 = 2 A21 = (–1)2+1 M21 = (–1)3 (–2) = 2 A22 = (–1)2+2 M22 = (–1)4 . 1 = 1 A23 = (–1)2+3 M23 = (–1)5 (–2) = 2 A31 = (–1)3+1 M31 = (–1)4 . 6 = 6 A32 = (–1)3+2 M32 = (–1)5 (–2) = 2 A33 = (–1)3+3 M33 = (–1)6 . 5 = 5 Thus, adj (B) = [■8(3&2&6@1&1&2@2&2&5)] Now, B−1 = 1/(|B|) adj (B) Putting values = 1/1 [■8(3&2&6@1&1&2@2&2&5)] = [■8(3&2&6@1&1&2@2&2&5)] Also, (AB)-1 = B−1 A−1 = [■8(3&2&6@1&1&2@2&2&5)] [■8(3&−1&1@−15&6&−5@5&−2&2)] = [■8(3(3)+2(⤶7−15)+6(−5)&3(−1)+2(6)+6(−2)&3(1)+2(−5)+6(2)@1(3)+1(⤶7−15)+2(−5)&1(−1)+1(6)+2(−2)&1(1)+1(−5)+2(2)@2(3)+2(⤶7−15)+5(−5)&2(−1)+2(6)+5(−2)&2(1)+2(−5)+5(2))] = [■8(9−30+30&−3+12−12&3−10+12@3−15+10&−1+6−4&1−5+4@6−30+25&−2+12−10&2−10+10)] = [■8(𝟗&−𝟑&𝟓@−𝟐&𝟏&𝟎@𝟏&𝟎&𝟐)]

Miscellaneous

Misc 1

Misc. 2 Important Deleted for CBSE Board 2021 Exams only

Misc 3

Misc 4

Misc 5

Misc 6 Important

Misc 7 Important You are here

Misc 8

Misc 9

Misc 10

Misc 11 Important Deleted for CBSE Board 2021 Exams only

Misc 12 Important Deleted for CBSE Board 2021 Exams only

Misc. 13 Deleted for CBSE Board 2021 Exams only

Misc 14 Deleted for CBSE Board 2021 Exams only

Misc. 15 Important Deleted for CBSE Board 2021 Exams only

Misc. 16 Important

Misc 17 Important Deleted for CBSE Board 2021 Exams only

Misc 18

Misc 19 Important

Matrices and Determinants - Formula Sheet and Summary

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.