InterviewSolution
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InterviewSolution
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निम्नलिखित प्रश्न तक प्रत्येक समीकरण निकाय को आव्यूह विधि से हल कीजिए। `2x=3y+3z=5,x-2y+z=-4,3x-y-2z=3` |
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Answer» दिया समीकरण निकाय `2x=3y+3z=5` `x-2y+z=-4` `3x-y-2z=3` `implies[(2,3,3),(1,-2,1),(3,-1,-2)][(x),(y),(z)]=[(5),(-4),(3)]impliesAX=B`……………1 `:.A=[(2,3,3),(1,-2,1),(3,-1,-2)]` `implies|A|=|(2,3,3),(1,-2,1),(3,-1,-2)|` `=2(4+1)-3(-2-3)+3(-1+6)` `=10+15+15=40!=0` `:.A` व्युत्क्रमणीय है। अब `A_(11)=5,A_(12)=5,A_(13)=5` `A_(21)=3,A_(22)=-13,A_(23)=11` `A_(31)=9,A_(32)=1,A_(33)=-7` `:.adjA[(5,5,5),(3,-13,11),(9,1,-7)]=[(5,3,9),(5,-13,1),(5,11,-7)]` तथा `A^(-1)=1/(|A|)adjA=1/40[(5,3,9),(5,-13,1),(5,11,-7)]` समीकरण 1 से `AX=BimpliesX=A^(-1)B` `implies[(x),(y),(z)]=1/40[(5,3,9),(5,-13,1),(5,11,-7)][(5),(-4),(3)]` `=1/40[(25-12+27),(25+52+3),(25-44-21)]=[(1),(2),(-1)]` `impliesx+1,y=2,z=-1` |
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