Could anyone double check my math?

Hey guys, I just get confused about the quiz in week 4.
The first one is question 6:

I do not know why only the columns of the full rank matrix could be consider the “span of the matrix”.

Also i understand what is the span of a linear space (i.e. 2d linear space = plane, 3d becomes 3D space), but what is the “span of a matrix”? I don’t think in the videos there is any description talking about it and gives the mathematical expression.

In addition to that, if the description is all correct (feedback description). Why is that the case that only columns are correct not the rows? Is there any difference between the matrix and its transpose in terms of the rank? Since the question is basically asking, if the rows are linearly dependent or the columns are linearly dependent.

The second question is about Q.7

I don’t think there is any correct answer, and the following is my deduction.

Re: question 6, I’ll pose this question to the course staff, and see what they think.
I agree, this material is very thinly covered in the lectures.

Re: question 7, I don’t have a reply.

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Also in Q7, I suspect that “contrust” should be “construct”.

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Hello @Jimmy0Jimmy,

I don’t mentor this course so I don’t comment on the quiz, but I am happy to double check your math.

If you have new steps to share and want someone to double check them, please let me know here.


Thank you Raymond, that is indeed helpful.

You are welcome, @Jimmy0Jimmy!

Stay curious and keep learning!