Science:Math Exam Resources/Courses/MATH221/December 2007/Question 03
Work in progress: this question page is incomplete, there might be mistakes in the material you are seeing here.
• Q1 • Q2 • Q3 • Q4 • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q6 (c) • Q7 (a) • Q7 (b) • Q7 (c) • Q8 (a) • Q8 (b) • Q8 (c) • Q8 (d) • Q9 (a) • Q9 (b) • Q9 (c) • Q9 (d) • QS101 10(a) • QS101 10(b) • QS102 10(a) • QS102 10(b) • QS102 10(c) • QS103 10(a) • QS103 10(b) • QS103 10(c) •
Question 03 

Find a 2 x 2 matrix A such that

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/December 2007/Question 03/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. Letting and , the task at hand is to solve for A. Now B and C are invertible matrices (as they have have nonzero determinant), so we can solve for A by multiplying the above equation on the left by , and on the right by , giving
It is straightforward to compute and . Therefore
