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Let A be the set of all $$3 \times 3$$ symmetric matrices all of whose entries are either 0 or 1. Five of these entries are 1 and four of them are 0.
Question 35
The number of matrices A in A for which the system of linear equations
$$A\begin{bmatrix}x\\y\\z \end{bmatrix} = \begin{bmatrix}1\\0\\0 \end{bmatrix}$$
is inconsistent, is
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