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2005 Brazil Undergrad MO Brazil Undergrad MO 2005 Day 1 October 22nd 1 Determine the number of possible values for the determinant of a matrix with real entries such that identity and is the all-zero matrix. , given that , where is is the cyshine view topic 2 Let and be two continuous, distinct functions from such that Let , for Prove that , natural. is an increasing and divergent sequence. aodeath view topic Click for solution Cezar Lupu view topic 3 Let vectors in such that . Prove that there exists a permutation every , . Remark: If , for of and such that for . cyshine view topic Day 2 October 23rd 4 Let and . Show that converge. IgorCastro view topic Click for solution alekk view topic 5 Prove that cyshine view topic Click for solution Kent Merryfield view topic 6 Prove that for any natural numbers matrix nonsingular. and , ,the ( cyshine view topic Click for solution ) is