Ex 4.6, 9 - Solve using matrix method 4x-3y=3 3x+5y=7 - Ex 4.6

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Ex 4.6, 9 Step 2 Calculate |A| |A| = 4﷮−3﷮3﷮−5﷯﷯ = 4(– 5) – 3 (– 3) = – 20 + 9 = – 11 ∴ |A| ≠ 0 ∴ System of equation is consistent & has a unique solution Now, AX = B X = A-1 B Step 3 Calculate X = A-1 B A-1 = 1﷮|A|﷯ adj (A) A = 4﷮−3﷮3﷮−5﷯﷯ adj A = 4﷮−3﷮3﷮−5﷯﷯ = −5﷮3﷮−3﷮4﷯﷯ Now, A-1 = 1﷮|A|﷯ adj A A-1 = 1﷮11﷯ −5﷮3﷮−3﷮4﷯﷯ Thus, X = A-1 B 𝑥﷮𝑦﷯﷯ = 1﷮11﷯ 5﷮−3﷮3﷮−4﷯﷯ 3﷮7﷯﷯ = 1﷮11﷯ 5 3﷯+ −3﷯7﷮3 3﷯+ −4﷯7﷯﷯ = 1﷮11﷯ 15−21﷮9−28﷯﷯ 𝑥﷮𝑦﷯﷯ = −6﷮11﷯﷮ −19﷮11﷯﷯﷯ Hence x = −𝟔﷮𝟏𝟏﷯ & y = −𝟏𝟗﷮𝟏𝟏﷯

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