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# W u is a subspace of v exploration questions these

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Unformatted text preview: Exploration questions These are questions testing your real understanding of the fundamentals. They are not a routine exercise since the solution process may not be obvious at ﬁrst glance. It may take a little bit of thought to ﬁgure out what to do; don’t be afraid to play around with some ideas. You’ll learn more by making mistakes and taking routes which lead to dead ends. Some of these questions may foreshadow upcoming material. E1. Lay 4.1 #26 E2. Deﬁne the trace of a matrix to be the sum of its diagonal entries. 1 MATH 895-4 Fall 2010 Course Schedule f a cu lty of science d epa r tm ent of m athema tic s Week Date Sections 1 Sept 7 2 14 I.4, I.5, I.6 5 Oct 5 III.1, III.2 6 12 7 19 8 26 9 Nov 2 Part/ References Topic/Sections MATH 240 H OMEWORK #4 Notes/Speaker from FS2009 (a) Show that trace : Mn,n → R is a linear transformation I.1, I.2, I.3 Symbolic Combinatorial (b) What is the range of trace : Mmethods R? n,n → Structures Unlabelled structures FS: (c) What is the Part A.1, A.2 of trace : M2,2 → R? kernel Comtet74 3 21 II.1, II.2, II.3 Labelled structures I Handout #1 E3. Lay 4.2 #30, 34 study) (self 4 28 II.4, II.5, II.6 Labelled structures II E4. Let V...
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