# FINALA - M340L FINAL EXAM A SPRING 2008 Dr Schurle Your...

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M340L FINAL EXAM A SPRING, 2008 Dr. Schurle Your name: Your UTEID: 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, . . . . THE EXAM HAS 12 PROBLEMS, EACH WORTH 10 POINTS. 1. In the process of solving the system of linear equations A x = b , you have done row operations to the augmented matrix [ A | b ] to obtain the following. Solve the system. 1 - 2 3 1 4 0 2 0 4 8 0 0 2 0 6 0 0 0 5 10

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2. Are the columns of the following matrix linearly independent? Show your work and explain your answer. 0 - 8 5 3 - 7 4 - 1 5 4 1 - 3 2 3. How many pivot columns must a 8 × 13 matrix A have in order that the columns of A span R 8 ? Explain your answer.
4. If A , B , and C are 8 × 8 invertible matrices, does the equation C - 1 ( A + X ) B - 1 = I 8 have a solution, X ? If so, ﬁnd it. If not, explain why not. 5. Recall that

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## This note was uploaded on 01/28/2009 for the course M 340L taught by Professor Pavlovic during the Fall '08 term at University of Texas.

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FINALA - M340L FINAL EXAM A SPRING 2008 Dr Schurle Your...

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