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Linear algebra riddle?
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<blockquote data-quote="Mozly" data-source="post: 2428983" data-attributes="member: 833381"><p>This is a bonus on my practice exam. Can you help me solve it?</p><p></p><p></p><p>Amy and Brian play a game in which they take turns filling the entries of an initially</p><p>empty 2010×2010 matrix. Amy plays first. At each turn, a player chooses a real number</p><p>and places it in a vacant entry. The game ends when the matrix is completely filled. Amy</p><p>wins if the resulting matrix is invertible, and Brian wins if the resulting matrix is not</p><p>invertible.</p><p>Which player has a winning strategy? Explain.</p></blockquote><p></p>
[QUOTE="Mozly, post: 2428983, member: 833381"] This is a bonus on my practice exam. Can you help me solve it? Amy and Brian play a game in which they take turns filling the entries of an initially empty 2010×2010 matrix. Amy plays first. At each turn, a player chooses a real number and places it in a vacant entry. The game ends when the matrix is completely filled. Amy wins if the resulting matrix is invertible, and Brian wins if the resulting matrix is not invertible. Which player has a winning strategy? Explain. [/QUOTE]
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