InterviewSolution
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InterviewSolution
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Write minros and cofactros of the elements of the determinants: (i) `|{:(1,0,4),(3,5,-1),(0,1,2):}|` |
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Answer» (i) `Let A=|{:(1,0,0),(0,1,0),(0,0,1):}|` Minors `M_(11)=|{:(1,0),(0,1):}|=1-0=1` `M_(12)=|{:(0,0),(0,1):}|=0-0=0,M_(13)=|{:(0,1),(0,0):}|=0-0=0` `M_(21)=|{:(0,0),(0,1):}|=0-0=0,M_(22)=|{:(1,0),(0,1):}|=1-0=0,` `M_(23)=|{:(1,0),(0,0):}|=0-0=0` `M_(33)=|{:(1,0),(0,1):}|=1-0=1 Cofactors` `A_(11)=(-1)^(1+1)M_(11)=1,A_(12)=(-1)^(1+2)M_(12)=0` `A_(13)=(-1)^(1+3)M_(13)=0` `A_(21)=(-1)^(2+1)M_(21)=0,A_(22)=(-1)^(2+2)M_(22)=1` `A_(23)=(-1)^(2+3)M_(23)=0` `A_(31)=(-1)^(3+1)M_(31)=0,A_(32)=(-1)^(3+2)M_(32)=0`, `A_(33)=(-1)^(3+3)M_(33)=1` `Let A= |{:(1,0,4),(3,5,-1),(0,1,2):}|` Minors `=|{:(5,-1),(1,2):}|=10+1=11,` `M_(12)=|{:(3,-1),(0,2):}|=6-0=6, M_(13)=|{:(3,5),(0,1):}|=3-0=3` `M_(23)=|{:(1,0),(0,1):}|=1-0=1` `M_(31)=|{:(0,4),(5,-1):}|=0-20-=-20` `M_(32)=|{:(1,4),(3,-1):}|=-1-12=-13`, `M_(33)=|{:(1,0),(3,5):}|=5-0=5` Cofactors `A_(11)=(-1)^(1+1)M_(11)=11` `A_(12)=(-1)^(2+1)M_(21)=4,A_(22)=(-1)^(2+2)M_(22)=2`, `A_(23)(-1)^(3+1)M_(31)=-20,A_(32)=(-1)^(3+2)M_(32)=13,` `A_(33)=(-1)^(3+3)M_(33)=5` |
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