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6. Let A = \begin{bmatrix} -3 & 6 & 4\\ 6 & -12 & 2 \end{bmatrix}, \mathbf{x} = \begin{bmatrix} x\\ y\\ z \end{bmatrix}, \mathbf{b} = \begin{bmatrix} 5\\ 10 \end{bmatrix}, \mathbf{y} = \begin{bmatrix} 2\\ -2\\ 5 \end{bmatrix} a) Write down the system of equations corresponding to A\mathbf{x} = \mathbf{b} \begin{bmatrix} -3 & 6 & 4\\ 6 & -12 & 2 \end{bmatrix} \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 5\\ 10 \end{bmatrix} b) Solve for \mathbf{x}. Leave your answer in parametric vector form. c) Is the solution set a subspace of \mathbb{R}^3? d) Calculate A\mathbf{y}.

          6. Let
A = \begin{bmatrix} -3 & 6 & 4\\ 6 & -12 & 2 \end{bmatrix}, \mathbf{x} = \begin{bmatrix} x\\ y\\ z \end{bmatrix}, \mathbf{b} = \begin{bmatrix} 5\\ 10 \end{bmatrix}, \mathbf{y} = \begin{bmatrix} 2\\ -2\\ 5 \end{bmatrix}
a) Write down the system of equations corresponding to A\mathbf{x} = \mathbf{b}
\begin{bmatrix} -3 & 6 & 4\\ 6 & -12 & 2 \end{bmatrix} \begin{bmatrix} x\\ y\\ z \end{bmatrix} = \begin{bmatrix} 5\\ 10 \end{bmatrix}
b) Solve for \mathbf{x}. Leave your answer in parametric vector form.
c) Is the solution set a subspace of \mathbb{R}^3?
d) Calculate A\mathbf{y}.

6. Let
A =
< b m a t r i x >
, 𝐱 =
< b m a t r i x >
, 𝐛 =
< b m a t r i x >
, 𝐲 =
< b m a t r i x >

a) Write down the system of equations corresponding to A𝐱 = 𝐛

< b m a t r i x >

< b m a t r i x >
=
< b m a t r i x >

b) Solve for 𝐱. Leave your answer in parametric vector form.
c) Is the solution set a subspace of ℝ^3?
d) Calculate A𝐲.

Added by Holly B.

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