Question

Rank-Nullity Question.
a) Give an example of a 3x3 matrix whose column space is a plane through the origin in 3-space.
b) What kind of geometric object is the null space of your matrix?
c) What kind of geometric object is the row space of your matrix?

Answer 1

For part a), would i need a 3x3 Matrix with all the contents = 0?

Answer 2

for a) the columns of a will have 2 linearly independent columns and 1 column, a scalar multiple of the other

Answer 3

the null space will have dimension of 1..so its a....

Answer 4

c) the RREF will have a row of 0s so the row space will have a dimension of 2..which is a...

Answer 5

hope i helped.

Answer 6

I am not clear.

Answer 7

which part?

Answer 8

what does it mean by the geometric object?

Answer 9

whether its a line or a plane or some other 3d complex shape

Answer 10

they would be s plane if the null space is 1 and if the row space is 2, correct?

Answer 11

it'll be a plane if dimension is 2 and a line if dimension is 1, so think again