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Unformatted text preview: Notes on linear algebra (Monday 17th October, 2016, 23:10) page 76 Proposition 3.44. Let a E N, m E IN and p E N. Let a 6 {1,2,...,a} and o E {1,2,...,m}. Let C be an m x p-matrix. Then, EHIflC is the a x p-matrix whose a-th row is the v-th row of C. and whose all other rows are filled with zeroes. (Here. again, Ear; means Emmfm.) a b (3 Example 3.45. Let a = 2, m = 3 and p = 3. Let C = a’ b’ c’ be a a” bf! CH 3 X 3-matrix. Proposition 3.44 (applied to a = 1 and U = 2) claims that ELZC is the 2 X 3-matrix whose 1-st row is the 2-nd row of C, and whose all other rows are filled with zeroes. In other words, it claims that a’b’c I We can verify this by actually doing the multiplication: a b c ELZC = ( g (1) g ) a“ l?! C! fl!!! lyxr r: c _ / 03+1HI+ORH Ob+1bi+0b” Oc+1ci+00”\ ...
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