The following system of equations x+y+z=9, 2x | vedclass

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(D) The given system of equations is:$x+y+z=9$$2x+5y+7z=52$$x+7y+11z=77$We represent this system as an augmented matrix $[A|B]$:$[A|B] = \begin{bmatri

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infinitely many solutions

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(D) The given system of equations is:$x+y+z=9$$2x+5y+7z=52$$x+7y+11z=77$We represent this system as an augmented matrix $[A|B]$:$[A|B] = \begin{bmatrix} 1 & 1 & 1 & 9 \ 2 & 5 & 7 & 52 \ 1 & 7 & 11 & 77 \end{bmatrix}$Applying row operations $R_2 ightarrow R_2-2R_1$ and $R_3 ightarrow R_3-R_1$:$\begin{bmatrix} 1 & 1 & 1 & 9 \ 0 & 3 & 5 & 34 \ 0 & 6 & 10 & 68 \end{bmatrix}$Applying row operation $R_3 ightarrow R_3-2R_2$:$\begin{bmatrix} 1 & 1 & 1 & 9 \ 0 & 3 & 5 & 34 \ 0 & 0 & 0 & 0 \end{bmatrix}$Here, the rank of the coefficient matrix $ho(A) = 2$ and the rank of the augmented matrix $ho(A|B) = 2$. Since $ho(A) = ho(A|B) < 3$ (where $3$ is the number of variables), the system has infinitely many solutions.

The following system of equations $x+y+z=9$, $2x+5y+7z=52$, $x+7y+11z=77$ has

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