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7.The sum of three times a number and 6 is 30.Find the number. |
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Answer» -STEP EXPLANATION:Given let a,b,c be the three numbers Then according to question a+b+c=6−−−−(1)a+3c=7−−−−−(2)3a+b+c=12−−−−−−−(3)Using determinant property for finding value of a,b,c we get.AX=B X=A −1 B⎣⎢⎢⎡ 113 101 131 ⎦⎥⎥⎤ ⎣⎢⎢⎡ abc ⎦⎥⎥⎤ = ⎣⎢⎢⎡ 6712 ⎦⎥⎥⎤ where A= ⎣⎢⎢⎡ 113 101 131 ⎦⎥⎥⎤ Now A −1 = ∣A∣adjA we know ∣A∣=1(0−3)−1(1−9)+1(1−0)∣A∣=−3+8+1∣A∣=6And adj A= ⎣⎢⎢⎡ −303 +8−2−2 1+2−1 ⎦⎥⎥⎤ adj A= ⎣⎢⎢⎡ −381 0−22 3−2−1 ⎦⎥⎥⎤ ⇒A −1 = 61 ⎣⎢⎢⎡ −381 0−22 3−2−1 ⎦⎥⎥⎤ Now⎣⎢⎢⎡ abc ⎦⎥⎥⎤ = 61 ⎣⎢⎢⎡ −381 0−22 3−2−1 ⎦⎥⎥⎤ ⎣⎢⎢⎡ 6712 ⎦⎥⎥⎤ = 61 ⎣⎢⎢⎡ −18486 +3−14+14 6−24−12 ⎦⎥⎥⎤ ⎣⎢⎢⎡ abc ⎦⎥⎥⎤ = 61 ⎣⎢⎢⎡ 18108 ⎦⎥⎥⎤ On comparing we get[a=3,b= 35 &c= 34 ] |
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