Grings - Álgebra Linear - Subespaço Vetorial - Ex4 - Aula 25

Linear Algebra Course - Vector Subspace Subscribe to my CHANNEL to receive FREE lessons WEBSITE: http://www.omatematico.com/ Lessons on DVD: http://www.lojaomatematico.com.br/ STUDYING has never been so easy! CONTENT:EXERCISE 1: Show that the subset of R^4 that is W = {(x, y, z, t) AND R^4 such that x + y = 0 and z - t = 0} is a subspace. (where: ^ is read as ) at time (0:40) There are 4 components (x, y, z, t), so it is R^4 at time (1:05) Remembering the 3 conditions for being a vector subspace: o E S você + v E S α u E S where α E R at time (1:29) Answer to exercise 1: W is a subspace of R^4 at time (14:24) EXERCISE 2: Verify if S = { (x, y, z) E R³ such that x E Z } is a vector subspace of the vector space V = R³ at time (14:42) Answer to exercise 2: S is not a vector subspace of V = R³ at time (21:09)