1.

Examine the consistency of the system of equations `x+3y=5 , 2x+6y=8`

Answer» Given system of equations
x+3y=5
2x+6y =8
`rArr" "|A|[{:(2,-1),(1,1):}][{:(x),(y):}]=[{:(5),(8):}]rArr AX=B`
`therefore" "A[{:(1,3),(2,6):}]`
`rArr" "|A|=[{:(1,3),(2,6):}]=6-6=0`
`therefore` A is non-invertible.
`"Now"" adj A="[{:(6,-3),(-2,1):}]`
`"Now adj A"=[{:(6,-3),(-2,1):}]`
`therefore" (adj A)B"=[{:(6,-3),(-2,1):}][{:(5),(8):}]`
`=[{:(30,-24),(-10,+8):}]=[{:(6),(-2):}]ne0`
`rArr` Given system of equations is inconsistent.


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