###### Exercise9

Determine whether the following statements are true or false and provide a justification for your response.

1. If $$A\xvec$$ is defined, then the number of components of $$\xvec$$ equals the number of rows of $$A\text{.}$$

2. The solution space to the equation $$A\xvec = \bvec$$ is equivalent to the solution space to the linear system whose augmented matrix is $$\left[\begin{array}{r|r} A \amp \bvec \end{array}\right]\text{.}$$

3. If a linear system of equations has 8 equations and 5 unknowns, then the dimensions of the matrix $$A$$ in the corresponding equation $$A\xvec = \bvec$$ is $$5\times8\text{.}$$

4. If $$A$$ has a pivot in every row, then every equation $$A\xvec = \bvec$$ is consistent.

5. If $$A$$ is a $$9\times5$$ matrix, then $$A\xvec=\bvec$$ is inconsistent for some vector $$\bvec\text{.}$$

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