The system of equations {x_1} + 2{x_2} + 3{x_ | vedclass

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(C) To determine the nature of the solution,we calculate the determinant $D$ of the coefficient matrix:$D = \begin{vmatrix} 1 & 2 & 3 \ 2 & 3 & 1 \

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Unique solution

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(C) To determine the nature of the solution,we calculate the determinant $D$ of the coefficient matrix:$D = \begin{vmatrix} 1 & 2 & 3 \ 2 & 3 & 1 \ 3 & 1 & 2 \end{vmatrix}$Expanding along the first row:$D = 1(3 	imes 2 - 1 	imes 1) - 2(2 	imes 2 - 3 	imes 1) + 3(2 	imes 1 - 3 	imes 3)$$D = 1(6 - 1) - 2(4 - 3) + 3(2 - 9)$$D = 1(5) - 2(1) + 3(-7)$$D = 5 - 2 - 21 = -18$Since $D 
eq 0$,the system of linear equations has a unique solution for any values of $a, b, c$.

The system of equations ${x_1} + 2{x_2} + 3{x_3} = a$,$2{x_1} + 3{x_2} + {x_3} = b$,and $3{x_1} + {x_2} + 2{x_3} = c$ has:

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