Math 1300: Tips for Distance Assignment 3 (classroom sections should take a look, too)

Published: Thu, 11/02/17

Grant's totally revised and augmented volume 2 of his Linear Algebra & Vector Geometry book is now available to order at UMSU Digital Print Centre, room 118 University Centre.
Try a Free Sample of Grant's Book and Audio Lectures
Don't have my book or audio?  You can download a free sample of my book and audio lectures containing Lessons 1 and 2:
Did you read my tips on how to study and learn this course?  If not, here is a link to those important suggestions:
Did you miss my Assignment 1 and my tips? Click here.
The department posted SOLUTIONS for Assignment 1 (these are not my solutions). Click here.
Did you miss my Assignment 2 and my tips? Click here.
The department posted SOLUTIONS for Assignment 2 (these are not my solutions). Click here.
Tips for Assignment 3
Here is a link to the actual assignment, for those of you who don't have it:
Study Lesson 9 (Vectors) and Lesson 10 (Lines and Planes) from my Linear Algebra & Vector Geometry, volume 2 book to prepare for this assignment.

Of course, always seek out assistance from my book, your course notes, etc. if you ever hit a question you don't understand, but try not to be learning things as you do an assignment.  Learn first, then put your learning to the test.
Question 1
This is a runthrough of all the concepts and examples I do in Lesson 10.  Most of my questions are very similar.
Question 2
A weird application of orthogonality as first introduced in Lesson 9 of my book.

Hint: You will only need to draw an ordinary, two-dimensional x-axis, y-axis graph if you follow the first condition he gives you correctly.  And, you may recall from high school that x^2+y^2=r^2 is a circle centred at (0,0) or radius r.
Question 3
Not unlike my Lesson 3, Lecture Problem 6.
Question 4
Revisiting properties of determinants, as taught in Lesson 6.
Question 5
Part 1
Recall: The definition of inverse is that a matrix multiplied by its inverse should equal the identity matrix.  This is saying that I-2A is its own inverse.  So, (I-2A) times (I-2A) should equal what?  Just do the matrix algebra (first discussed back in Lesson 3) and see what happens.  Remember, you have been told, in this case, that A^2 = A.

Part 2
Use the Equivalent Statements Theorem, as listed on page 189 in Lesson 6.  There are several things you could do here.  Determinants might help, but, personally, I would consider inverses.