Did you read my tips on how to study and learn Math 1310?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 1?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 2?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 3?  If not, here is a link to those important suggestions:

Did you read my Tips for Assignment 4?  If not, here is a link to those important suggestions:

Here is a link to the actual assignment, in case you don't have it handy:

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 free sample of my book and audio lectures containing Lessons 1 and  2:

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.

This is not unlike my examples in Lesson 11. 

The method I use to solve my Lesson 11, question 4(b) may help you understand what to do for your question 2(b).

Note that, when they put vertical lines around an expression (like absolute value signs), as in 2(c), that is what I would denote with double lines. In other words, |PR + QR| is what I would denote ||PR + QR||, which means they want the length or norm of PR + QR.

I define the nullspace in my Lesson 14, questions 3 and 4.

The easiest way to do this question is to transpose the given vector in each part and call that transpose vector x.  Then check if Ax = 0.  If and only if, the answer is "yes", the given vector must be in the nullspace.

This is more like my Lesson 14, questions 3 and 4.

Very similar to my questions in Lesson 12.  Feel free to do this question open-book using similar examples from my book.  Very unlikely you will ever have to do this kind of thing on your exam.

This 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.

Make sure you have studied the Linear Independence section in Lesson 13 of my book and gone through my question 4 in that lesson.  Hint: you can use a determinant to solve this problem.  Note that it is also quite similar to my Lesson 6, question 5.  If you find it difficult to solve for k using determinants, you might prefer to use the row-reduction method to prove independence/dependence.  That makes it similar to my Lesson 2, questions 6 to 8.  How many solutions must the augmented matrix you set up have, if the vectors are to be linearly dependent?

Very similar to my Lesson 13, questions 1 and 2.