From Lecture 7: How can we say that the linear combination of free column number of vectors obtained by keeping special values for free columns will always be a Null space. In the example described where we had two free vectors, why the professor did not consider special values as (1,1) but has considered both (1,0) and (0,1) as special values.

Question

From Lecture 7: How can we say that the linear combination of free column number of vectors obtained by keeping special values for free columns will always be a Null space.  In the example described where we had two free vectors, why the professor did not consider special values as (1,1) but has considered both (1,0) and (0,1) as special values.

anonymous · Answer

because (1,1)=(1,0)+(0,1), and all other vectors in the space will be equal to combination of (1,0) and (0,1)

anonymous · Answer

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