. Consider the points , , and . Find the point S in whose third component is 6 and such that is parallel to .

Math 340 Lecture – Introduction to Ordinary Differential Equations – February 29 , 2016 th What We Covered: 1. Course Content – Chapter 7: Matrix Algebra a. Section 7.5: Bases of a Subspace Continued i. Recap 1. Nullspace: () = ∶ = 0 ℝ 2. Definition: a subspace ℝ such that a. If , then x+y e V b. If xeV, ℝ then 3. Null(A) is a subspace of ℝ 4. Linear dependence and independence a. Definition: the vectors ,…, ℝ are linearly independent is 1 1 1 ⋯+ = + ⋯+1 = 0 ii. Example: are = (1,0) and = (0,1) linearly independent 1 2 ℎ 1 2ℝ ℎ ℎ 1 1 2 2 1,0 + 0,1 = (0,0)