Answer to Question #311135 in Linear Algebra for Jlove

Question

Let V = set of all 3x1 matrices.

Define

+ to be the matrix addition

⦁ to be the matrix multiplication by a number

We know that V is a vector space. If W [a, b, 1] , a, b element of R then W is a subspace of V.

Answer 1

$\vec{x_1}=[a_1,b_1,1]\in W, a_1,b_1\in R\\ \vec{x_2}=[a_2,b_2,1]\in W, a_2,b_2\in R\\$

$1. \vec{x_1}+\vec{x_2}=[a_1,b_1,1]+[a_2,b_2,1]=\\ =[a_1+a_2,b_1+b_2,2]\not\in W$

W is not a subspace of V.