Example 13 - Chapter 3 Class 12 Matrices
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 13 If A = [■8(1&−2&3@−4&2&5)] and B = [■8(2&3@4&5@2&1)] then find AB, BA . Show that AB ≠ BA AB =[■8(1&−2&3@−4&2&5)]_(2 × 3 ) [■8(2&3@4&5@2&1)]_(3 × 2) = [■8(𝟏 × 𝟐+(−𝟐) × 𝟒+𝟑 × 𝟐&𝟏 × 𝟑+(−𝟐) × 𝟓+𝟑 × 𝟏@−𝟒 × 𝟐+𝟐 × 𝟒+𝟓 × 𝟐&−𝟒 × 𝟑+𝟐 × 𝟓+𝟓 × 𝟏)]_(𝟐 × 𝟐 ) = [■8(2−8+6&3−10+3@−8+8+10&−12+10+5)] = [■8(𝟎&−𝟒@𝟏𝟎&𝟑)] . BA = [■8(2&3@4&5@2&1)]_(3 × 2) [■8(1&−2&3@−4&2&5)]_(2 × 3) = [■8(𝟐 × 𝟏+𝟑 × (−𝟒)&𝟐 × (−𝟐)+𝟑 × 𝟐&𝟐 × 𝟑+𝟑 × 𝟓@𝟒 × 𝟏+𝟓 × (−𝟒)&𝟒 × (−𝟐)+𝟓 × 𝟐&𝟒 × 𝟑+𝟓 × 𝟓@𝟐 × 𝟏+𝟏 × (−𝟒)&𝟐 × (−𝟐)+𝟏 × 𝟐&𝟐 × 𝟑+𝟏 × 𝟓)]_(𝟑 × 𝟑 ) = [■8(2−12&−4+6&6+15@4−20&−8+10&12+25@2−4&−4+2&6+5)] = [■8(−𝟏𝟎&𝟐&𝟐𝟏@−𝟏𝟔&𝟐&𝟑𝟕@−𝟐&−𝟐&𝟏𝟏)] ≠ AB Hence AB ≠ BA
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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo