Question

Consider the following system of linear equations $2x_1 - x_2 = \lambda x_1$ $2x_1 - x_2 + x_3 = \lambda x_2$, $\lambda \in \mathbb{R}$. $-2x_1 + 2x_2 + x_3 = \lambda x_3$ Which of the following is the augmented matrix of the given system? $\begin{pmatrix} 2 & -1 & \lambda & 0 \\ 2 & (-1 + \lambda) & 1 & 0 \\ -2 & 2 & 1 & \lambda \end{pmatrix}$ $\begin{pmatrix} 2 & -1 & 0 & \lambda \\ 2 & (-1 - \lambda) & 1 & 0 \\ -2 & 2 & (1 - \lambda) & 1 \end{pmatrix}$ $\begin{pmatrix} 2 & -1 & 0 & \lambda \\ 2 & -1 & 1 & \lambda \\ -2 & 2 & 1 & \lambda \end{pmatrix}$ $\begin{pmatrix} (2 - \lambda) & -1 & 0 \\ 2 & (-1 - \lambda) & 1 \\ -2 & 2 & (1 - \lambda) \end{pmatrix}$

          Consider the following system of linear
equations
$2x_1 - x_2 = \lambda x_1$
$2x_1 - x_2 + x_3 = \lambda x_2$, $\lambda \in \mathbb{R}$.
$-2x_1 + 2x_2 + x_3 = \lambda x_3$
Which of the following is the augmented
matrix of the given system?
$\begin{pmatrix} 2 & -1 & \lambda & 0 \\ 2 & (-1 + \lambda) & 1 & 0 \\ -2 & 2 & 1 & \lambda \end{pmatrix}$
$\begin{pmatrix} 2 & -1 & 0 & \lambda \\ 2 & (-1 - \lambda) & 1 & 0 \\ -2 & 2 & (1 - \lambda) & 1 \end{pmatrix}$
$\begin{pmatrix} 2 & -1 & 0 & \lambda \\ 2 & -1 & 1 & \lambda \\ -2 & 2 & 1 & \lambda \end{pmatrix}$
$\begin{pmatrix} (2 - \lambda) & -1 & 0 \\ 2 & (-1 - \lambda) & 1 \\ -2 & 2 & (1 - \lambda) \end{pmatrix}$

Consider the following system of linear
equations
2x1 - x2 = λ x1
2x1 - x2 + x3 = λ x2, λ∈ℝ.
-2x1 + 2x2 + x3 = λ x3
Which of the following is the augmented
matrix of the given system?
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Added by Joshua H.

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