**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.“ ...

View
Full Document

- Fall '08
- Staff
- Linear Algebra, Algebra