(A) The system of equations can be represented as $AX = B$,where $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \\ 5 & 5 & 9 \end{bmatrix}$.To determine

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(A) The system of equations can be represented as $AX = B$,where $A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 1 & 3 \\ 5 & 5 & 9 \end{bmatrix}$.To determine the nature of the solution,we calculate the determinant $\Delta = |A|$.$\Delta = 1(9-15) - 2(18-15) + 3(10-5)$$\Delta = 1(-6) - 2(3) + 3(5)$$\Delta = -6 - 6 + 15 = 3$.Since $\Delta \neq 0$,the system of equations has a unique solution (only one solution).

Class 12 Mathematics 3 and 4 .Determinants and Matrices Solution of the Linear equations using Matrices

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For the equations $x+2y+3z=1$,$2x+y+3z=2$,and $5x+5y+9z=4$,which of the following is true?

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A
there is only one solution
B
there exists infinitely many solutions
C
there is no solution
D
None of the above

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