{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# Exam1B - x in R 3 for which T x = 5(16 points After many...

This preview shows pages 1–5. Sign up to view the full content.

M340L EXAM 1B SPRING, 2010 Dr. Schurle Show all your work on these pages. Be organized and neat. Your work should be your own; there should be no talking, reading notes, checking laptops, using cellphones, . . . . 1. (14 points) Describe in detail the method used to determine whether p vectors in R q are linearly independent and explain why the method works.

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

View Full Document
YOUR SCORE: /100 2. (14 points) Suppose A and D are matrices, not necessarily square, such that AD = I p . Explain why the equation A x = b has a solution for every b in R p and then explain what this says about the columns of A . 3. (14 points) Find the inverse of D = " 2 1 3 2 # and use it to solve X - " 1 2 3 4 #! D = " 2 2 1 3 # for X .
4. (14 points) Suppose the linear transformation T from R 3 to R 2 maps x = x 1 x 2 x 3 into x 1 " 3 9 # + x 2 " 1 4 # + x 3 " 2 2 # . (a) Calculate and simplify T 1 2 3 . (b) Find a matrix A such that T ( x ) = A x . (c) Use parametric vector form to describe the collection of all

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 in R 3 for which T ( x ) = . 5. (16 points) After many row operations you have changed the matrix A to the following, which is not yet in reduced echelon form. Describe all solutions of the system A x = in parametric vector form. DO NOT USE A CALCULATOR!! SHOW ALL YOUR WORK STEP BY STEP!!! 3 2 13 1 24 11-2 1-4-3-3 1 0 3 4 2 1 0 3-1 2-1 6. (14 points) Do the columns of the following matrix span all of R 3 ? Justify your answer. 1 3 8 4-2-2-17-6 4 35 10 7. (14 points) Write the coeﬃcient matrix that results from using the vector equation ap-proach to balance the following chemical reaction. DO NOT SOLVE THE SYSTEM!! NaHCO 3 + H 3 C 6 H 5 O 7 → Na 3 C 6 H 5 O 7 + H 2 O + CO 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