• 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 (f) 

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.) Let be the columns of A. Express as a linear combination of the columns of 
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 (f)/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.) To express as a linear combination of and , we take n multiples of each vector that will add up to . 2.) One way to do this is by putting the vectors in a system of equations and then putting this system of equations into an augmented matrix: + 2  2 = 4 0+ + 3 = 2 0 + 0 + = 2
3.) Reduce to row echelon form through these steps: 1.) = 3 2.) = + 2 3.) =  2 and you will get: 4.) This shows the linear combination: = 24 = 8 = 2 = 24  8 + 2 PROOF: = 24  8+ 2 =  + 