For the system of equations: x + 2y + 3z = 1 2x + y + 3z = 2 5x + 5y + 9z = 4

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KollegeApply · Accepted Answer

(a) there is only one solution The given system of equations can be written in matrix form as follows: \begin{bmatrix}1 & 2 & 3 \ 2 & 1 & 3 \ 5 & 5 & 9\end{bmatrix}\begin{bmatrix}x \ y \ z\end{bmatrix} = \begin{bmatrix}1 \ 2 \ 4\end{bmatrix} Here, A=\begin{bmatrix}1 & 2 & 3 \ 2 & 1 & 3 \ 5 & 5 & 9\end{bmatrix},X=\begin{bmatrix}x \ y \ z\end{bmatrix}	ext{ and }B = \begin{bmatrix}1 \ 2 \ 4\end{bmatrix} Now, \left| A ight| = \begin{vmatrix}1 & 2 & 3 \ 2 & 1 & 3 \ 5 & 5 & 9\end{vmatrix} = 1\left( 9 - 15 ight) - 2\left( 18 - 15 ight) + 3\left( 10 - 5 ight) = - 6 - 6 + 15 = 3 
eq 0 \Rightarrow \left| A ight|
eq 0 So, the given system of equations has a unique solution.

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