{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

quiz1_S06

# quiz1_S06 - x 1-x 2 = 1 x 1 kx 2-4 x 3 = 3-x 1 2 x 2(1 k x...

This preview shows pages 1–6. Sign up to view the full content.

Princeton University Department of Mathematics Name: Instructor: Class time: MAT 202 – Linear Algebra with Applications QUIZ 1 – Spring 2006 This quiz is due Friday, March 3, at 2 pm at your instructor’s office. You have 60 minutes to complete your work. Please show all work and write neatly. Each of the five problems corresponds to 10 points. Books, notes, calculators, computers are not permitted on the quiz. As part of your obligations under the Honor Code, do not discuss this quiz with anyone until after the Friday 2 pm deadline. WRITE OUT AND SIGN THE PLEDGE: I pledge my honor that I have not violated the Honor Code during this examination. for the grading problem score 1 2 3 4 5 total

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

View Full Document
2 (1) Solve the following system: x 1 + 2 x 2 + x 3 + x 4 = 1 2 x 1 + 2 x 2 - x 3 - x 4 = 0 x 1 - 2 x 2 - 5 x 3 + x 4 = 0 What is the rank of the corresponding coefficient matrix and what is the rank of the corresponding augmented matrix?
3 (2) For what values of k does the following system:

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

View Full Document

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: x 1-x 2 = 1 x 1 + kx 2-4 x 3 = 3-x 1 + 2 x 2-(1 + k ) x 3 = 0 have (a) inﬁnitely many solutions? (b) no solutions? (c) exactly one solution? Justify your answers and provide a brief geometric interpretation. 4 (3) Find the matrix A of the orthogonal projection onto the plane x 1-x 2 + x 3 = 0 . Describe geometrically the transformation given by A 2 . Is A invertible? 5 (4) Find the inverse of the matrix A = 1 1 4 1 2 3 1 6 (5) Determine whether the following statements are true or false. No explanations, no credit. (a) Given two square matrices A and B , if AB is invertible, then so is A . (b) The composition of a shear, a reﬂection and a rotation in the plane is invertible. (c) There exist matrices A of size 3 × 2 and B of size 2 × 3 such that AB = I 3 is the identity matrix....
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