If begin{bmatrix} 1 & 1 & 1 1 & -2 & -2 1 & | vedclass

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(D) The given matrix equation is equivalent to the following system of linear equations: $x + y + z = 0$ $\dots (i)$ $x - 2y - 2z = 3$ $\dots (ii)$ $x

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$-3$

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(D) The given matrix equation is equivalent to the following system of linear equations: $x + y + z = 0$ $\dots (i)$ $x - 2y - 2z = 3$ $\dots (ii)$ $x + 3y + z = 4$ $\dots (iii)$ Subtracting equation $(i)$ from equation $(iii)$: $(x + 3y + z) - (x + y + z) = 4 - 0$ $2y = 4 \implies y = 2$ Substitute $y = 2$ into equations $(i)$ and $(ii)$: $x + 2 + z = 0 \implies x + z = -2$ $\dots (iv)$ $x - 2(2) - 2z = 3 \implies x - 2z = 7$ $\dots (v)$ Subtracting equation $(v)$ from equation $(iv)$: $(x + z) - (x - 2z) = -2 - 7$ $3z = -9 \implies z = -3$ Substitute $z = -3$ into equation $(iv)$: $x - 3 = -2 \implies x = 1$ Now,calculate $2x - y + z$: $2(1) - 2 + (-3) = 2 - 2 - 3 = -3$

If $\begin{bmatrix} 1 & 1 & 1 \\ 1 & -2 & -2 \\ 1 & 3 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 0 \\ 3 \\ 4 \end{bmatrix}$,then $2x - y + z = $

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