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(B) The augmented matrix for the system is: $\left[\begin{array}{cccc}1 & 1 & -1 & 1 \ 2 & 4 & -1 & 0 \ 3 & 4 & 5 & 18\end{array}ight]$ Apply row

Vedclass · Accepted Answer

$4$

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(B) The augmented matrix for the system is: $\left[\begin{array}{cccc}1 & 1 & -1 & 1 \ 2 & 4 & -1 & 0 \ 3 & 4 & 5 & 18\end{array}ight]$ Apply row operations: $R_2 	o R_2 - 2R_1$: $\left[\begin{array}{cccc}1 & 1 & -1 & 1 \ 0 & 2 & 1 & -2 \ 3 & 4 & 5 & 18\end{array}ight]$ $R_3 	o R_3 - 3R_1$: $\left[\begin{array}{cccc}1 & 1 & -1 & 1 \ 0 & 2 & 1 & -2 \ 0 & 1 & 8 & 15\end{array}ight]$ $R_3 	o 2R_3 - R_2$: $\left[\begin{array}{cccc}1 & 1 & -1 & 1 \ 0 & 2 & 1 & -2 \ 0 & 0 & 15 & 32\end{array}ight]$ Comparing this with the given matrix $\left[\begin{array}{cccc}1 & a & 0 & -1 \ 0 & 2 & 1 & b \ 0 & 0 & c & 32\end{array}ight]$, we observe the target form requires $R_1$ to have $0$ in the third column. Performing $R_1 	o R_1 + R_2$ (using the modified $R_2$): $\left[\begin{array}{cccc}1 & 3 & 0 & -1 \ 0 & 2 & 1 & -2 \ 0 & 0 & 15 & 32\end{array}ight]$ Thus, $a = 3$, $b = -2$, and $c = 15$. Then $\sqrt{a+b+c} = \sqrt{3 - 2 + 15} = \sqrt{16} = 4$.

If the augmented matrix corresponding to the system of equations $x+y-z=1$, $2x+4y-z=0$ and $3x+4y+5z=18$ is transformed to $\left[\begin{array}{cccc}1 & a & 0 & -1 \\ 0 & 2 & 1 & b \\ 0 & 0 & c & 32\end{array}\right]$, then $\sqrt{a+b+c}=$

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