1.

Examine the consistency of the system of equations`x" "+" "y" "+" "z" "=" "1``2x" "+" "3y" "+" "2z" "=" "2``a x" "+" "a y" "+" "2a" "z" "=" "4`

Answer» Given system of equations,
x+y+z=1
2x+3y+2z=1
ax+ay+2az = 4
`rArr" "[{:(1,1,1),(2,3,2),(a,a,2a):}][{:(x),(y),(z):}]=[{:(1),(1),(4):}]rArrAX=B`
`therefore" "A=[{:(1,1,1),(2,3,2),(a,a,2a):}]`
`rArr" "|A|=[{:(1,1,1),(2,3,2),(a,a,2a):}]`
=1(6a-2a)-1(4a-2a)+1(2a-3a)
`= 4a-2a-a=ne0`
`therefore` A is invertible.
`rArr` Given system of equations is consistent.


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