MathDB

1

Part of 2004 IMC

Problems(2)

Problem 1 IMC 2004 Macedonia

Source:

7/25/2004
Let SS be an infinite set of real numbers such that ∣x1+x2+⋯+xn∣≤1|x_1+x_2+\cdots + x_n | \leq 1 for all finite subsets {x1,x2,…,xn}⊂S\{x_1,x_2,\ldots,x_n\} \subset S. Show that SS is countable.
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Problem 7 IMC 2004 Macedonia

Source:

7/26/2004
Let AA be a real 4×24\times 2 matrix and BB be a real 2×42\times 4 matrix such that AB=(10−10010−1−10100−101). AB = \left(% \begin{array}{cccc} 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & -1 \\ -1 & 0 & 1 & 0 \\ 0 & -1 & 0 & 1 \\ \end{array}% \right). Find BABA.
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