{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

e208fk

This preview shows pages 1–2. Sign up to view the full content.

MAS 3105 Sept 19, 2008 Quiz 2 Prof. S. Hudson 1) [20pt] Find the determinants of these matrices. If possible, find quick ways to do them (without using the definition) and explain briefly. A = 1 2 3 0 5 6 0 0 7 B = 0 0 7 0 5 6 1 2 3 C = 1 2 1 2 3 2 1 2 1 2) [20pt] Solve for X given that AX + B = X and A = 0 1 0 - 1 B = - 2 - 2 6 8 3) [20pt] Choose one of these HW proofs; you can answer on the back: A) If A is row equivalent to both B and to C , then B is row equivalent to C . B) Suppose these 3 matrices are all nxn, and AB = C . Prove: if B is singular, then C is, too. Bonus: (about 5 points) Almost the same as part 3B, But prove: if A is singular, then C is, too. Hint: transpose. Remarks and Answers : I was short of time, and based this Quiz on one from Spring 2007. The average was about 47/60. The scale for this quiz is: A-’s start at 54, B-’s at 48, C-’s at 42, etc). 1) det A = 35, det B = -35, det C = 0. 2) From ( A - I ) X = - B , multiply by on the LEFT to get X = - ( A - I ) - 1 B = see below. If you multiplied on the right, and made no other mistakes, you should get the matrix

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Y instead (which got about 12 points of partial credit). X = ± 1 2 3 4 ² Y = ±-2-2 6 7 ² I’d strongly suggest checking your answer - which should be much easier than solving the problem. 3) These were HW problems from Ch 1. I already have answers or hints posted on this site, but if you need more help, you can always see me. Bonus: Suppose A is singular and C = AB . Then A T is singular, because det A T = det A = 0 [or, we could justify this step without determinants, using Exercise 17 of Ch 1.3). 1 So, B T A T is singular (by problem 3b above, since the A T is on the right side). So, the transpose of this is singular, namely AB . Done. Note: Transposes have many purposes, and this proof shows one of them - to swap the left and right factors in a product. 2...
View Full Document

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern