Ex 3.2, 10 - Chapter 3 Class 12 Matrices

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Ex 3.2,10 Solve the equation for x, y, z and t, if 2[■8(𝑥&𝑧@𝑦&𝑡)] + 3 [■8(1&−1@0&2)] = 3 [■8(3&5@4&6)] 2[■8(𝑥&𝑧@𝑦&𝑡)] + 3 [■8(1&−1@0&2)] = 3 [■8(3&5@4&6)] [■8(𝑥×2&𝑧×2@𝑦×2&𝑡×2)] + [■8(1×3&−1×3@0×3&2×3)] = [■8(3×3&5×3@4×3&6×3)] [■8(2𝑥&2𝑧@2𝑦&2𝑡)] + [■8(3&−3@0&6)] = [■8(9&15@12&18)] [■8(2𝑥+3&2𝑧−3@2𝑦+0&2𝑡+6)] = [■8(9&15@12&18)] [■8(𝟐𝒙+𝟑&𝟐𝒛−𝟑@𝟐𝒚&𝟐𝒕+𝟔)] = [■8(𝟗&𝟏𝟓@𝟏𝟐&𝟏𝟖)] Since matrices are equal. Corresponding elements are equal 2x + 3 = 9 2y = 12 2z – 3 = 15 2t + 6 = 18 Solving equation (1) 2x + 3 = 9 2x = 9 – 3 x = 6/2 x = 3 Solving equation (2) 2y = 12 y = 12/2 y = 6 Solving equation (3) 2z – 3 = 15 2z = 15 + 3 z = 18/2 z = 9 Solving equation (4) 2t + 6 = 18 2t = 18 – 6 t = 12/2 t = 6 Hence x = 3 , y = 6 , z = 9 & t = 6