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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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.
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 :
Then and thus .