2 Suppose matrix A is mn and that v and w both solve Ax 0 S

2. Suppose matrix A is m×n, and that v and w both solve Ax = 0. Show that v + w must also solve Ax = 0

Solution

As v and w both are solutions for Ax = 0, that means:

Av = 0and Aw = 0

now, A(v+w) = Av + Aw.

=> A(v+w) = 0 + 0

=>  A(v+w) = 0

Therefore it is proved that, v+w must solve Ax = 0