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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 17 corresponding entry of the row vector CB. Hence, rowi (AB) equals CB. Thus, rowi (AB) = ESE—J B = (rowl- A) + B. This proves Proposition 2.19 (c). =rowI-A (d) The proof of Proposition 2.19 (d) is similar to that of Proposition 2.19 (e). Let me nevertheless show it, for the sake of completeness. (The proof below is essentially a copy-pasted version of the above proof of Proposition 2.19 (c), with only the necessary changes made. This is both practical for me. as it saves me some work, and hopefully helpful for you, as it highlights the similarities.) Let j E {1,2, . . . , p}. Set D = colj- B. Notice that D is a column vector of size 111, thus an m X 1-matrix. We can refer to any given entry of D either as ”the i-th entry" or as ”the (1', 1)-th entry” (where 1' is the number of the row the entry is located in). We have BL} BZJ D = coli B = ' 3...};- Thus Del 2 Bka' for every k E {1.2, . . . .m} . (12) Leti 6 {1,2,. . .,n}. Then, (+11“ ';_-I*l‘\ mini-1417 n-F HA1. 1" d. If.“ ...
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