1.

Express the following equations in matrix form and solve them by the method of reduction : `x+y+z=6,3x-y+3z=6and5x+5y-4z=3`.

Answer» Matrix form of the given equations is
`[{:(1,1,1),(3,-1,3),(5,5,-1):}][{:(x),(y),(z):}]=[{:(6),(6),(3):}]`
Applying `R_(2)toR_(2)-3R_(1)andR_(3)toR_(3)-5R_(1)`
`[{:(1,1,1),(0,-4,0),(0,0,-9):}][{:(x),(y),(z):}]=[{:(6),(-12),(-27):}]`
`[{:(x+,y+,z),(,-4y,),(,-9z,):}]=[{:(6),(-12),(-27):}]`
`:.` We get, `x+y+z=6" "......(i)`
`-4y=-12" "......(ii)`
`-9z=-27" "......(iii)`
From equation (ii), we get y =3
From equation (iii), we get z=3.
Substituting y=3 and z=3 in equation (i), we get x =0.
`:.x=0,y=3` and z=3 is the required solution.


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