Consider the system of linear equations:
`x_(1) + 2x_(2) + x_(3) = 3`
`2x_(1) + 3x_(2) + x_(3) = 3`
`3x_(1) + 5x_(2) + 2x_(3) = 1`
The system has

Options

A. Infinite number of solutions
B. Exactly three solutions
C. A unique solution
D. No solution

Answer

D

Explanation

Here `A=[(1,2,1),(2,3,1),(3,5,2)],B=[(3),(3),(1)]`
Now `|A|=1(6-5)-2(4-3)+1(10-9)`
`=1-2+1=0`
Now `adjA=[(C_(11),C_(12),C_(13)),(C_(21),C_(22),C_(23)),(C_(31),C_(32),C_(33))]^(T)=[(1,-1,1),(1,-1,1),(-1,1,-1)]^(T)`
Now `(adjA)B=[(1,1,-1),(-1,-1,1),(1,1,-1)][(3),(3),(1)]=[(5),(-5),(5)]!=0`
Hence the given system of equations in inconsistent and has no solution.