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Show that the equation $Ax=b$ is not consistent for all possible $b$, and describe the set of all $b$ for which the equation is consistent, both algebraically and geometrically.

$A = \begin{bmatrix} 1& 3& -4\\ -2& 1& 2\\ 3 &2& -6 \end{bmatrix}$

$b = \begin{bmatrix}b_1\\b_2\\b_3\end{bmatrix}$

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HINT: Set up the augmented matrix,

$\left[\begin{array}{rrr|r} 1&3&-4&b_1\\ -2&1&2&b_2\\ 3&2&-6&b_3 \end{array}\right]\;,$

and do a row reduction. The numbers have been chosen to make it very easy.

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    Thanks so much! This was a great help.2012-09-05