If p, q, r are 3 real numbers satisfying the | vedclass

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(A) Given the matrix equation: $[p, q, r] \begin{bmatrix} 3 & 4 & 1 \ 3 & 2 & 3 \ 2 & 0 & 2 \end{bmatrix} = [3, 0, 1]$Performing matrix multiplicati

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$-3$

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(A) Given the matrix equation: $[p, q, r] \begin{bmatrix} 3 & 4 & 1 \ 3 & 2 & 3 \ 2 & 0 & 2 \end{bmatrix} = [3, 0, 1]$Performing matrix multiplication,we get:$[3p + 3q + 2r, 4p + 2q, p + 3q + 2r] = [3, 0, 1]$Equating the corresponding elements,we obtain the following system of linear equations:$1) 3p + 3q + 2r = 3$$2) 4p + 2q = 0 \Rightarrow q = -2p$$3) p + 3q + 2r = 1$Subtracting equation $(3)$ from equation $(1)$:$(3p + 3q + 2r) - (p + 3q + 2r) = 3 - 1$$2p = 2 \Rightarrow p = 1$Substituting $p = 1$ into $q = -2p$:$q = -2(1) = -2$Substituting $p = 1$ and $q = -2$ into equation $(3)$:$1 + 3(-2) + 2r = 1$$1 - 6 + 2r = 1$$-5 + 2r = 1 \Rightarrow 2r = 6 \Rightarrow r = 3$Now,calculate $2p + q - r$:$2(1) + (-2) - 3 = 2 - 2 - 3 = -3$.

If $p, q, r$ are $3$ real numbers satisfying the matrix equation $[p, q, r] \begin{bmatrix} 3 & 4 & 1 \\ 3 & 2 & 3 \\ 2 & 0 & 2 \end{bmatrix} = [3, 0, 1]$,then $2p + q - r$ equals

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