Answer to Question #91405 in Linear Algebra for Sajid

Question

Choose the correct answer.
Q.If M and N are 3 dimensional subspaces of R^6, then what is possible dimension of subspace M∩N?
a. 2,3,4,6
b. 1,2,3,4
c. 0,1,2,3
d. 3,4,5,6

Answer 1

Since M∩N is a subspace for both M and N, then the dimension of M∩N can't be greater than the dimension of M, N, therefore the dimension of M∩N can be 0,1, 2, 3, the answer is c). 0, 1, 2, 3.