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[answered] Math 125 - Section B1, Fall 2016 Assignment #9 Due: Wednesd


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Math 125 ? Section B1, Fall 2016

 

Assignment #9

 

Due: Wednesday, Nov. 30, 2016

 

Please submit your assignment through Crowdmark by 11pm on the due date.

 

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

 

6

 

0 ?2 2 ?3 0 Question 1. Let A = . Find det(A) in two ways:

 

2

 

0 ?2

 

0

 

4 ?2 5

 

3

 

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 b

 

a + 4c b + 4d a) If C =

 

and det(C) = 2, find det .

 

c d

 

a

 

b

 

" # " b) Let A and B be 3 ? 3 matrices. If det(AT ) = 4 and det(2A?1 B 3 ) = 54. Find:

 

i) det(B)

 

ii) det(adj(A))

 

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

 

1 1

 

1

 

1

 

0 1

 

1

 

2

 

2 ?1 x1

 

0 1 x2 0 = .

 

1 x3 0

 

1

 

x4

 

1 This system has a unique solution. Use Cramer?s rule to find x3 .

 


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