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Question 05 (b) 

Let Let T denote a linear transformation of R^{2} such that Find T(b_{3}) and give the matrix of T with respect to the standard basis of R^{2} 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

To find T(b_{3}) express b_{3} as a linear combination of b_{1} and b_{2}. Then use the linearity of T. 
Hint 2 

To find the matrix representation of T you need to calculate T(e_{1}) and T(e_{2}), where e_{1} = [1,0] and e_{2} = [0,1]. Again, linear combinations and linearity of T will be your friends. 
Checking a solution serves two purposes: helping you if, after having used all the hints, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Since we have that To find the matrix of T with respect to the standard basis, we need to compute the image of each of these standard vectors. and And so the matrix of T in the standard basis is
