Science:Math Exam Resources/Courses/MATH221/December 2007/Question 05 (a)
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Question 05 (a) 

Find the determinant of the matrix

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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 05 (a)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Recall that adding multiples of one row to another does not change the determinant. So to make our lives easier when calculating the determinant of B, we will simplify by row reduction as much as possible. Subtracting the first row from the second, third, and fourth, results in the matrix
whose determinant is the same as B. Now subtracting twice the second row from the third, and three times the second row from the fourth, gives
whose determinant is still equal to that of B. A final step is to subtract 3/2 times the third row from the fourth to have
This matrix is uppertriangular, so we know how to calculate its determinant: it is simply the product of the diagonal entries. We therefore conclude that
