MAT 1341 Lecture 3: Fundamental Theory of Algebra and Vector Geometry
23 Sep 2016
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Lecture 3: fundamental theorem of algebra and vector. Gauss completed the first proof for this theorem which states: Every polynomial with complex coefficients can be factored using complex numbers. We can keep going like this eg. space-time. Therefore, for any number, n, in the natural number set: 2. 2 algebraic structure of zero vector: 0 = (cid:894)0, ,0(cid:895) + +kmum is called a linear combination of u1, ,um. 1*(1,2,3) + 7*(1,0,0) = (8,2,3) is a linear combination of u1 and u2. Observe that (0,1,0) is not a linear combination of u1 and u2: (0,1,0) = k1(1,2,3) + k2(1,0,0) When solving for k1 and k2, the second and third equations contradict each other, and so (0,1,0) is not a linear combination of u1 and u2. 2. 4 properties of vector addition and scalar multiplication. V2 adding identity ( ) that is: v+0=v. V4 commutativity v+w=w+v for: u, v, w and k, m. These rules are also known as the vector spaces axioms.
