Ex 4.6, 6 - Chapter 4 Class 12 Determinants

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Ex 4.6, 6 Examine the consistency of the system of equations. 5x − y + 4z = 5 2x + 3y + 5z = 2 5x − 2y + 6z = −1 The system of equations is 5x − y + 4z = 5 2x + 3y + 5z = 2 5x − 2y + 6z = −1 Step 1 Write about equation as AX = B 5﷮−1﷮4﷮2﷮3﷮5﷮5﷮−2﷮6﷯﷯ 𝑥﷮𝑦﷮𝑧﷯﷯ = 5﷮2﷮−1﷯﷯ Hence A = 5﷮−1﷮4﷮2﷮3﷮5﷮5﷮−2﷮6﷯﷯, X = 𝑥﷮𝑦﷮𝑧﷯﷯ & B = 5﷮2﷮−1﷯﷯ Step 2 Calculate |A| |A| = 5﷮−1﷮4﷮2﷮3﷮5﷮5﷮−2﷮6﷯﷯ = 5 3﷮5﷮−2﷮6﷯﷯ – 1 ( –1) 2﷮5﷮5﷮6﷯﷯ + 4 2﷮3﷮5﷮−2﷯﷯ = 5 (18 + 10) + 1(12 – 25) + 4( – 4 – 15) = 5 (28) + 1 ( –13) + 4( – 19) = 140 – 13 – 78 = 51 ≠ 0 Since |A| ≠ 0 The given system of equation is consistent