Linear Algebra Matrices problem

[needhelpp]

can someone please help explain this linear algebra problem to me. I am completely lost on how to find the values of the matrix only given the column space and null space.

 

[Steven G]

You have to follow our guidelines and show us where you are stuck. This is an excellent problem!

Can you tell us what the basis for the column space of A means and why there are only 2 vectors in that basis?

Can you tell us what the basis for the null space of A means and what it means when there are only 3 vectors in that basis?

You can't do this problem until you have a good understand of those definitions.

Please post back with your answer. Thanks.

 

[needhelpp]

the column space is the span of all the linear combinations of the column vectors.
the null space describes the relationship between the columns in the matrix and how they relate to each other

 

[needhelpp]

I determined that the first column in the matrix should be all zeros based on the first value of the null space

 

[Steven G]

That is NOT the definition of the null space at all? Look up the definition in your book!

I agree that the 1st column should be 0 but what definition did you use for null space to get that result. You failed to answer all my questions.

What can you say about some of the columns of A? Are any of them all 0's? Why/Why not??