Science:Math Exam Resources/Courses/MATH221/December 2011/Question 05 (a)
• Q1 (a) • Q1 (b) • Q2 (a) • Q2 (b) • Q3 (a) • Q3 (b) • Q4 (a) • Q4 (b) • Q5 (a) • Q5 (b) • Q6 (a) • Q6 (b) • Q7 • Q8 (a) • Q8 (b) •
Question 05 (a) 

Find the standard matrix of the linear transformation of R^{3} which reflects across the yzplane. 
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 

What does this transformation do to the three basis vectors [1,0,0], [0,1,0], and [0,0,1]? 
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. To find the standard matrix of this linear transformation, we simply consider the image of the three base vectors. The vector [1, 0, 0] is sent to the vector [1, 0, 0] and the vectors [0, 1, 0] and [0, 0, 1] simply remain where they are (since they belong to the yzplane itself). Hence the standard matrix of this linear transformation is 