Give an example of a 3 times 3 matrix whose column space is

Give an example of a 3 times 3 matrix whose column space is a plane through the origin in R^3. What kind of geometric object is the nullspace of your matrix? Explain your answer. What kind of geometric object is the row space of your matrix? Explain your answer.

Solution

a> if there is a 3x3 matrix whose two columns are linearly independent then we\'ll have a column space that is a plane passing through the origne.

A = [1 2 3]

       [4 5 6]

       [7 8 9]

b> the dimension of the null space would be = 1 . The null space would be a line passing through the orign.

c> the row space would be 1 dimensional in nature and hence would be a line passing through the origin.