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Math 125 ? Section B1, Fall 2016
Due: Wednesday, Nov. 30, 2016
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Show your work. Stating the final solution is not enough. It should be clear how you determined the
answer from the work you provide. 3
0 ?2 2 ?3 0 Question 1. Let A = . Find det(A) in two ways:
4 ?2 5
a) using cofactor expansion along the row or column of your choice, and
b) by applying elementary row / column operations to A to obtain a triangular matrix. Question 2.
a + 4c b + 4d a) If C =
and det(C) = 2, find det .
" # " b) Let A and B be 3 ? 3 matrices. If det(AT ) = 4 and det(2A?1 B 3 ) = 54. Find:
c) Suppose that P is an n ? n matrix such that P T P 3 = I, where I is the n ? n identity matrix.
i) Find all possible values of det(P ). Justify your answer.
ii) Is P invertible? Justify your answer. 1 1
Question 3. Consider the linear system 0
2 ?1 x1
0 1 x2 0 = .
1 x3 0
1 This system has a unique solution. Use Cramer?s rule to find x3 .
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