Use matrix method to show that the system that the system of equation
`2x+5y=7`
`6x+15y=13`
is inconsistent

Explanation

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