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Ex 4.6, 8 - Solve using matrix method 2x - y = -2, 3x+4y=3 - Find solution of equations- Equations given

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  1. Chapter 4 Class 12 Determinants
  2. Serial order wise
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Step 2 Calculate |A| |A| = 2﷮−1﷮3﷮4﷯﷯ = 2(4) – (– 1)(3) = 8 + 3 = 11 ∴ |A| ≠ 0 Thus, 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 = 2﷮−1﷮3﷮4﷯﷯ adj A = 2﷮−1﷮3﷮4﷯﷯ = 4﷮1﷮−3﷮2﷯﷯ Now, A-1 = 1﷮|A|﷯ adj A A-1 = 1﷮11﷯ 4﷮1﷮−3﷮2﷯﷯ Thus, X = A-1 B 𝑥﷮𝑦﷯﷯ = 1﷮11﷯ 4﷮1﷮−3﷮2﷯﷯ −2﷮3﷯﷯ = 1﷮11﷯ 4 −2﷯+1(3)﷮−3 −2﷯+2(3)﷯﷯ 𝑥﷮𝑦﷯﷯ = 1﷮11﷯ −8+3﷮6+6﷯﷯ = 1﷮11﷯ −5﷮12﷯﷯ 𝑥﷮𝑦﷯﷯ = −5﷮11﷯﷮ 12﷮11﷯﷯﷯ Hence, x = −𝟓﷮𝟏𝟏﷯ & y = 𝟏𝟐﷮𝟏𝟏﷯

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