Science:Math Exam Resources/Courses/MATH307/December 2012/Question 03 (a)
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q1 (a) • Q1 (b) • Q1 (c) • Q1 (d) • Q1 (e) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q3 (c) • Q3 (d) • Q3 (e) • Q4 (a) • Q4 (b) • Q4 (c) • Q4 (d) • Q4 (e) • Q5 (a) • Q5 (b) • Q5 (c) • Q5 (d) • Q6 (a) • Q6 (b) • Q6 (c) • Q6 (d) • Q6 (e) • Q6 (f) •
Question 03 (a) 

Let be the subspace of vectors in whose components sum to zero. (a) Find a matrix A so that S is the null space of A, i.e., S = N(A). 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

How are the row space and the nullspace of of a matrix related? 
Hint 2 

The nullspace of a matrix A is the orthogonal complement of the row space. Can you find a vector orthogonal to S? 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. The definition of S contains a dot product which reveals the vector orthogonal to S: Since the vector is orthogonal to S, and the nullspace of A ( which is S) is orthogonal to the row space of A, we can choose any matrix A whose row space is spanned by . Such as or 