Science:Math Exam Resources/Courses/MATH152/April 2013/Question A 13
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Question A 13 |
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The linear transformation is given by for some matrix . Given that and , find the matrix M. |
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 |
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You might try to write the two given matrix-vector equations as a single matrix equation. Then you will see M can be determined via a matrix multiplication problem. |
Hint 2 |
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Remember the formula for the inverse of a 2-x-2 matrix: provided . |
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.
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Solution 1 |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Notice that you can write the two given matrix-vector equations as a matrix-matrix equation: Since M times the matrix of vectors is the 2-x-2 identity matrix, this means that Using the 2-x-2 inverse matrix formula, we can write |
Solution 2 |
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Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. Since M is a linear transformation, and Hence |