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2x-y+3z=9x+y+z=6x-y+z=2 |
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Answer» -STEP explanation:Given2x−y+3z=9 ………..(1)x+y+z=6 …………..(2)x−y+z=2 …………….(3)using matrix inversion methodAX=B⎣⎢⎢⎡ 211 −11−1 311 ⎦⎥⎥⎤ ⎣⎢⎢⎡ XYZ ⎦⎥⎥⎤ = ⎣⎢⎢⎡ 962 ⎦⎥⎥⎤ and X=A −1 B where A −1 = ∣A∣adj(A) Now adjA= ⎣⎢⎢⎡ 20−2 −2−1−1 −413 ⎦⎥⎥⎤ ∣A∣=2(1+1)−1(1−1)+3(−1−1)∣A∣=4−6∣A∣=−2.Now A −1 = 2−1 ⎣⎢⎢⎡ 20−2 −2−1−1 −413 ⎦⎥⎥⎤ Now X=A −1 B⎣⎢⎢⎡ xyz ⎦⎥⎥⎤ = 2−1 ⎣⎢⎢⎡ 20−2 −2−1−1 −413 ⎦⎥⎥⎤ ⎣⎢⎢⎡ 962 ⎦⎥⎥⎤ ⎣⎢⎢⎡ xyz ⎦⎥⎥⎤ = 2−1 ⎣⎢⎢⎡ 18−12−80−6+2−18−6+6 ⎦⎥⎥⎤ = 2−1 ⎣⎢⎢⎡ −2−4−18 ⎦⎥⎥⎤ ⎣⎢⎢⎡ xyz ⎦⎥⎥⎤ = ⎣⎢⎢⎡ 129 ⎦⎥⎥⎤ HENCE [x=1,y=2 & z=9]. |
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