The no of rows for the matrices which describe the spaces should be the same
example of a subspace in R4 where components add upto zero
Let V , W be vectors of this subspace
V+W =[v1+w1,v2+w2,..,v4+w4] the components still add upto zero
cV+dW even scaled the vector components still add upto zero
Find a matrix whose multiplication with v gives the equation v1+v2+v3+v4=0
[1 1 1 1] *V ⇒ v1+v2+v3+v4 = 0
therefore the solution set of the null space of this matrix gives MV=0
Rank of this matrix is 1 and the dimension of null space is 4-1 (n-r) = 3
Reduced row echolon form is the same matrix [1 1 1 1]
