MAT224H1 Lecture Notes - Lecture 1: Scalar Multiplication, Euclidean Vector, Additive Inverse
Document Summary
Math 224 multiplication & then check all of 1)-10) hold. Notes: for (cid:1848) to be vector space, need to know/be given operations of vector add & scalar. (cid:3041) with respect to component-wise addition & scalar multiplication. (cid:3040) (cid:3041)(cid:4666) (cid:4667) = set of all (cid:1865) (cid:1866) matrices with real entries w. r. t. entry-wise addition & (cid:3041)(cid:4666) (cid:4667) = set of all polynomials of (cid:1856)(cid:1857) (cid:1866) with real coefficients. Answer: no, ac fails. w. r. t. usual polynomial addition & scalar multiplication (degree-wise). scalar multiplication. Something unusual: ac v, 2) cv check 3)-10) also hold. Proof: assume (cid:882) & (cid:882) are two vectors in (cid:1848). Show 0 = 0" then 0" + 0 = 0" since 0 is zero vector (by z) the zero vector is unique then 0 + 0" = 0 since 0" is zero vector (by z) & by c: 0 + 0" = 0" + 0 => 0 = 0 + 0" = 0" + 0 = 0"
