###### Exercise6

Consider the matrix

\begin{equation*} A=\left[\begin{array}{rrrr} 1 \amp 2 \amp -4 \amp -4 \\ 2 \amp 3 \amp 0 \amp 1 \\ 1 \amp 0 \amp 4 \amp 6 \\ \end{array}\right]\text{.} \end{equation*}
1. Find the product $$A\xvec$$ where

\begin{equation*} \xvec = \fourvec{1}{-2}{0}{2}\text{.} \end{equation*}
2. Give a description of the vectors $$\xvec$$ such that

\begin{equation*} A\xvec = \threevec{-1}{15}{17}\text{.} \end{equation*}

3. Find the reduced row echelon form of $$A$$ and identify the pivot positions.

4. Can you find a vector $$\bvec$$ such that $$A\xvec=\bvec$$ is inconsistent?

5. For a general 3-dimensional vector $$\bvec\text{,}$$ what can you say about the solution space of the equation $$A\xvec = \bvec\text{?}$$

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