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Unformatted text preview: Notes on linear algebra (Monday 17th October. 2016. 23:10) page 77 Example 3.47. Let us demonstrate Proposition 3.46 on a more spartanic example: Let n = 2, mt = 2 and p = 1. Let C = ( a b ) be a 1 X 2-matrix. Proposition 3.46 (applied to a = 1 and U = 2) claims that C512 is the 1 X 2-matrix whose 2-nd column is the 1-st column of C, and whose all other columns are filled with zeroes. In other words, it claims that CE1!2=(0 fl). Again, we can verify this by actually doing the multiplication: crmzm a)“ é)=(at0+b-O a—1+b*0)=(0 a). 3.7. (*) A bit more on the standard matrix units Let us get some practice by rewriting the definition of the matrices Em: Proposition 3.48. Let a E ]N and m E IN. Let a E {1.2,...,n} and v E {1,2,...,m}. Leti E {1,2,...,a} andj E {1,2,. . .,m}. Then, (Eu 7]): : : (5H «H In ml. : 51' “(51' 71 (60) ...
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