1.

Solve by matrix method : `2x+y=5` `x-y = 1`

Answer» Write the given equations in matrix form
`[{:(2,1),(1,-1):}][{:(x),(y):}]=[{:(5),(1):}]`
`rArr" " AX=B`
`"Where "A=[{:(2,1),(1,-1):}],X=[{:(x),(y):}]" and B"=[{:(5),(1):}]`
`|A|=[{:(2,1),(1,-1):}]=-2-1 =-3 ne0`
`therefore" A is invertible",`
Cofactors of the elements of matrix A.
`c_(11)=(-1)^(1+1)(-1)=-1`
`x_(12)=(-1)^(1+2)1=-1`
`c_(21)=(-1)^(2+1)1=-1`
`c_(22)=(-1)^(2+2)2=2`
`therefore" adj. A"=[{:(c_(11),c_(12)),(c_(21),c_(22)):}]`
`[{:(-1,-1),(-1,2):}]=[{:(-1,-1),(-1,2):}]`
`"and "A^(-1)=1/(|A|)" adj. A"=-1/3[{:(-1,-1),(-1,2):}]`
Now AX=B
`rArr" "AX=B`
`rArr[{:(x),(y):}]=-1/3[{:(-1,-1),(-1,2):}]=-1/3[{:(-5,-1),(-5,+2):}]=[{:(2),(1):}]`
`therefore" "x=2, y=1.`


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