Let M be a 3 × 3 matrix such that M pmatrix 1 0 0 pmatrix = pmatrix...

Let $M$ be the matrix whose columns are the given vectors. We have:

$M = \begin{pmatrix} 1 & 0 & -1 \\ 2 & 1 & 1 \\ 3 & 2 & 1 \end{pmatrix}$

Given $M \begin{pmatrix} x \\ y \\ z \end{pmatrix} = \begin{pmatrix} 1 \\ 7 \\ 11 \end{pmatrix}$, we can write this as a system of linear equations:

$x - z = 1$

$2x + y + z = 7$

$3x + 2y + z = 11$

Subtracting the second equation from the third equation gives:

$x + y = 4$

Adding the first equation and the second equation gives:

$3x + y = 8$

Subtracting the equation $x + y = 4$ from $3x + y = 8$ gives:

$2x = 4 \Rightarrow x = 2$

Substituting $x = 2$ into $x + y = 4$ gives:

$2 + y = 4 \Rightarrow y = 2$

Substituting $x = 2$ into $x - z = 1$ gives:

$2 - z = 1 \Rightarrow z = 1$

Therefore, $x + y + z = 2 + 2 + 1 = 5$.

Answer: $5$