Ex 4.6, 7 - Solve using matrix method 5x + 2y = 4, 7x + 3y = 5 - Ex 4.6

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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ex 4.6 Step 2 Calculate |A| |A| = 5﷮2﷮7﷮3﷯﷯ = 5(3) – 7 15 – 14 = 15 – 14 = 1 ∴ |A| ≠ 0 Since |A|≠ 0, System of equations is consistent & has a unique solution Now, AX = B Solution is X = A-1 B Step 3 Calculate X = A-1 B A-1 = 1﷮|A|﷯ adj (A) A = 5﷮2﷮7﷮3﷯﷯ adj A = 5﷮2﷮7﷮3﷯﷯ = 3﷮−2﷮−7﷮5﷯﷯ Now, A-1 = 1﷮|A|﷯ adj A Putting values = 1﷮−1﷯ 3﷮−2﷮−7﷮5﷯﷯ = 3﷮−2﷮−7﷮5﷯﷯ & B = 4﷮5﷯﷯ Now X = A-1 B 𝑥﷮𝑦﷯﷯ = 3﷮−2﷮−7﷮5﷯﷯ 4﷮5﷯﷯ 𝑥﷮𝑦﷯﷯ = 3 4﷯+ −2﷯5﷮−7 4﷯+5(5)﷯﷯ 𝑥﷮𝑦﷯﷯ = 2﷮−3﷯﷯ Hence x = 2 & y = –3

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