Science:Math Exam Resources/Courses/MATH221/December 2009/Question 02 (b)
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Question 02 (b) 

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 2009/Question 02 (b)/Hint 1 
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Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Strategy: Use the following determinant properties. The determinant of upper triangular matrix (i.e a matrix in row echelon form in this case) is equal to the product of its diagonal entries. If ij , then subtracting some constant time row i from row j does not change the determinant. Step 1: Perform the following row operations on B: row 2 = row 2  2 row 1 row 3 = row 3  2 row 1 and we get
Since the above matrix is still not in upper triangular form, perform the following row operations to it: row 3 = row 3  2 row 2 row 4 = row 4  3 row 2 Then we get:
After performing one more row operation, row 4 = row 4 + 5 row 3, we get the following upper triangular matrix:
Step 2 : Let Then and thus . 