Science:Math Exam Resources/Courses/MATH221/April 2010/Question 01 (h)
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) • Q1 (f) • Q1 (g) • Q1 (h) • Q2 (a) • Q2 (b) • Q2 (c) • Q3 (a) • Q3 (b) • Q4 • Q5 • Q6 • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q9 • Q10 • Q11 • Q12 (a) • Q12 (b) •
Question 01 (h) 

Let and Then the matrix U is an echelon form for A (you may assume this, you don't have to do the row reduction again.) Find all solutions to the system of equations
(Hint: What is the augmented matrix for this system?) 
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 hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

Science:Math Exam Resources/Courses/MATH221/April 2010/Question 01 (h)/Hint 1 
Checking a solution serves two purposes: helping you if, after having used the hint, 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. 1.) Transform the system of equations into an augmented matrix. x,y,z,&w all represent one column each and the number of system of equations represent the rows of the matrix. The answers to each equation will be on the rightmost of the matrix. 2.) 3.) Let’s reduce it to row echelon form by following these steps: 1. = 2 + 2. = 1 + 3. = 1 + 4. = 2 + 5. = 1 + 6. = 3 + 7. = 2 + 8. = 2 + and we will end up with The right most values in column 5 are the answers. 4.) Therefore, the system of equations correspond to: = + 24 = 2  8 = = 2 All solutions are represented by: = 