Science:Math Exam Resources/Courses/MATH221/December 2008/Question 03 (b)
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Question 03 (b) 

Find the determinant of the matrix . 
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 

Use part (a) to save some calculation. Think about what the effect on the determinant is when one row is multiplied by a number c. 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. We want to make use of the result of 3a. The given matrix A is not in the right form to use the formula of 3a. However by multiplying the first row by 1/3, and multiplying the third row by 1/10 will give us the desired form with x = 1, y = 5, and z = 7. More precisely,
Recall that multiplying a row of a matrix by a number c changes the determinant by a factor of c. For this question, this means that
By 3a, . So . 