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MAT 1332 Lecture Notes - Lecture 5: Commutative Property, List Of Forgotten Realms Nations, Row And Column Vectors

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School
University of Ottawa
Department
Mathematics
Course
MAT 1332
Professor
Weixuan Li

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Document Summary

This session covers complex numbers (continued), vectors and matrices: find z = i. Hence: find cos , where is the angle between vectors u = (1, 1, 1) and v = (2, 1, 2). || u || = 3 , || v || = 3. u v = 1. 3 3: find the product of matrices: (i) For which value(s) of a and b does matrix a b. Note that matrix multiplication does not satisfy the commutative law in general. 1: let m = [aij]m n = a. , and let b be a column vector x = x. 2 x n (i) find mx. (ii) let cj be the j-th column of m. write mx as a linear combination of cj j = 1, 2, , n. Solution. (i) m is m n, and x is n 1. The product is am m 1 matrix, or a column vector: 2 2 m a x mn n a x.

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