InterviewSolution
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InterviewSolution
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Use matrix method to show that the system that the system of equation `2x+5y=7` `6x+15y=13` is inconsistent |
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Answer» The given equation are `2x+5y=7 " " …(i)` `6x+15y=13 " " (i)` Let `A=[{:(2" 5 "),(6 " 15 "):}], X=[{:(x),(y):}] and B=[{:(7),(13):}]` Then the given system in matrix from is AX `ne` O. Now, `|A|=[{:(2" 5 "),(6 " 15 "):}]=0` The system will be inconsistent if (adjA) B `ne` O The minors of the elements of |A| are `M_(11)=15," " M_(12)=6` `M_(21)=5 " " M_(22)=2` So the confactors of the elements of |A| are `A_(11)=15," " A_(12)=-6` `A_(21)=-5 " " A_(22)=2` `therefore adjA=[{:(15 " -6") ,(-5 " "2) :}]=[{:(15 " -5") ,(-6 " "2) :}]` `rArr (adjA)B=[{:(15 " -6") ,(-5 " "2) :}] [{:(7),(13):}]=[{:(105 " -65") ,(-42 ""+26) :}]=[{:(" "40),(-16):}] ne O` Thus |A|=0 and (adjA)B `ne` O. Hence , the given system of equation is inconsistant |
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