Note that you need to study Lesson 11 (Vectors), Lesson 12 (Vector Spaces and Subspaces), Lesson 13 (Linear Independence), and Lesson 14 (Basis and Dimension) from my Matrices for Management book to prepare for this assignment.

 

Don't have my book? You can download a sample containing two free lessons here:

Grant's Tutoring Study Guides (Including Free Samples) 

 

Here is a link where you can download part of my lesson on Equations of Lines from my Linear Algebra book to assist you with question 1 in the assignment.

Question 2 is not unlike my examples in Lesson 11.  Note that, when they put vertical lines around an expression (like absolute value signs), as in 2(c), that is what I would denote ||PR + QR||.  In other words, that means they want the length or norm of PR + QR.

 

Question 3 is quite easy really.  As I teach in Lesson 14, the null space of A is the set of vectors X, such that AX = 0.  Simply write the given vector as a column and compute AX (multiply the matrix A to the transpose of the given vector X).  If the answer is the zero vector, 0, then X is in the null space of A.  If the answer is non-zero, or not even defined, then X is not in the null space of A.

 

Question 5 is similar to my examples in Lesson 12.

 

Question 6 is back to Lesson 11 again.  Just do what you are told.  Again, they mean the norm of u + kv. Set up the equation and solve k.