Science:Math Exam Resources/Courses/MATH152/April 2010/Question B 04 (e)
• QA 1 • QA 2 • QA 3 • QA 4 • QA 5 • QA 6 • QA 7 • QA 8 • QA 9 • QA 10 • QA 11 • QA 12 • QA 13 • QA 14 • QA 15 • QA 16 • QA 17 • QA 18 • QA 19 • QA 20 • QA 21 • QA 22 • QA 23 • QA 24 • QA 25 • QA 26 • QA 27 • QA 28 • QA 29 • QA 30 • QB 1(a) • QB 1(b) • QB 1(c) • QB 2(a) • QB 2(b) • QB 3(a) • QB 3(b) • QB 3(c) • QB 3(d) • QB 4(a) • QB 4(b) • QB 4(c) • QB 4(d) • QB 4(e) • QB 5(a) • QB 5(b) • QB 6(a) • QB 6(b) • QB 6(c) • QB 6(d) • QB 6(e) •
Question B 04 (e) 

The augmented matrix below for a linear system is put in reduced row echelon form with row operations. Write one of the following:
(e) 
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 

When we have more columns that rows in a matrix, what do we know about the number of free variables? 
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. For the matrix, we have two more columns than rows (the matrix is rank deficient) and so we have two free variables. Let x_{3} and x_{4} be those variables. Then from row 2 we have, and from row 1 we have, Therefore we have two null vectors, and as well as a particular solution Therefore the solution is There are an infinite number of solutions. 