Addition/ subtraction of matrices
Last updated at April 16, 2024 by Teachoo
Ex 3.2,10 Solve the equation for x, y, z and t, if 2[โ 8(๐ฅ&๐ง@๐ฆ&๐ก)] + 3 [โ 8(1&โ1@0&2)] = 3 [โ 8(3&5@4&6)] 2[โ 8(๐ฅ&๐ง@๐ฆ&๐ก)] + 3 [โ 8(1&โ1@0&2)] = 3 [โ 8(3&5@4&6)] [โ 8(๐ฅร2&๐งร2@๐ฆร2&๐กร2)] + [โ 8(1ร3&โ1ร3@0ร3&2ร3)] = [โ 8(3ร3&5ร3@4ร3&6ร3)] [โ 8(2๐ฅ&2๐ง@2๐ฆ&2๐ก)] + [โ 8(3&โ3@0&6)] = [โ 8(9&15@12&18)] [โ 8(2๐ฅ+3&2๐งโ3@2๐ฆ+0&2๐ก+6)] = [โ 8(9&15@12&18)] [โ 8(๐๐+๐&๐๐โ๐@๐๐&๐๐+๐)] = [โ 8(๐&๐๐@๐๐&๐๐)] Since matrices are equal. Corresponding elements are equal 2x + 3 = 9 2y = 12 2z โ 3 = 15 2t + 6 = 18 Solving equation (1) 2x + 3 = 9 2x = 9 โ 3 x = 6/2 x = 3 Solving equation (2) 2y = 12 y = 12/2 y = 6 Solving equation (3) 2z โ 3 = 15 2z = 15 + 3 z = 18/2 z = 9 Solving equation (4) 2t + 6 = 18 2t = 18 โ 6 t = 12/2 t = 6 Hence x = 3 , y = 6 , z = 9 & t = 6