Math 1300: Tips for Distance Assignment 3

Published: Thu, 10/18/12


 
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Here are some tips to help you with Assignment 3 if you are taking Math 1300 via distance/online.
 
You will need to study Lesson 2 (Row-Reduction and Linear Systems) to prepare for assignment 3.
 
Question 1 is just a runthrough of the definitions for RREF and REF given right at the start of my lesson.  Note that none of the 4 conditions demand that there be leading 1's in an echelon form matrix. Only if there are nonzero rows must the first nonzero value be a 1.  Also realize that there is no law that says a leading 1 must be in the top left corner.  You are merely required that each nonzero row begin with a leading 1, and that the leading 1's appear deeper in the row each time as you go down the rows.
 
Question 2 is classic Gauss-Jordan elimination like my question 3 in Lesson 2.
 
Note that question 3 has given you an augmented matrix, so you may want to draw a vertical line to separate the last column from the others.  This is similar to my question 1 in Lesson 2.  Note that, when they ask how many independent variables are there, they are asking how many parameters are there.
 
Question 4 is similar to my questions 6, 7 and 8 in Lesson 2.
 
You should find my question 9 in Lesson 2 quite helpful when you are solving question 5.  Feel free to use a calculator on this question if the decimals prove too much for you.
 
Question 6 is scary, but not as hard as it looks.  As I point out in my question 2 of Lesson 2, if you are given a solution to an equation, then sub it into the equation.  For example, you are told that (x0, y0,z0) is a solution to the first equation, so sub those values in place of x, y and z to get:
 
ax0 + by0 + cz0 = d
 
You can do similarly for the other solution you are given for equation (1) and for the solution you have been given for equation (2).
 
Then, if part (a) is correct, apparently what they gave you is a solution to equation (2).  However, you must prove that it is a solution to equation (2).  Which is to say, you must prove that:
a(x0 - x1)+ b(y0 - y1) + c(z0 - z1) = 0
 
Hint: Take the two solutions you noted for equation 1 earlier and line them up directly underneath each other in columns (you will have an "a" column, a "b" column, and a "c" column equal to a "d" column on the right side of the two equations.  Then subtract each column.  Factor a out of the first pair of terms, b out of the second pair, and c out of the third pair.  And you should be very pleased with the result.
 
You will use similar methods for parts (b) and (c).