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M340L EXAM 1A FALL, 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, . . . . 1. (18 points) After many row operations you have changed the augmented matrix of a system of linear equations to the following, which is not yet in reduced echelon form. Describe all solutions of the system in parametric vector form. 1 3 2 4 1 0 0 1 - 2 3 0 0 - 2 4 - 6

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YOUR SCORE: /100 2. (12 points) Write down the augmented matrix for the system of equations that describe the following network ﬂow. DO NOT SOLVE THE EQUATION!!!! 3. (18 points) Are the columns of the following matrix linearly independent? Show your work and explain your answer. 1 3 0 3 - 1 - 1 - 1 1 0 - 4 2 - 8 1 0 3 - 1
4. (18 points) For which value(s) of h do the following vectors span

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Unformatted text preview: R 3 ? Show your work and explain your answer. 1-1-3 , -5 6 8 , 1 1 h 5. (a) (6 points) Let A be a 7 4 matrix. What must a and b be in order to dene a linear transformation T : R a R b by T ( x ) = A x ? (b) (8 points) Let T : R 2 R 2 be a linear transformation for which T &quot; 1 #! = &quot; 2 3 # and T &quot; 1 #! = &quot; 5-2 # . Find T &quot;-1 3 #! . 6. Let A = &quot; 3 2 1 1 # and B = &quot;-2 1 1-1 # . Compute or nd or answer the following. (a) (3 points) 3 A + 2 B (b) (3 points) A T B T (c) (3 points) AB (d) (5 points) The fourth column of AC , where C is a 2 9 matrix whose fourth column is &quot; 1 1 # . (e) (6 points) Is there a 2 2 matrix D whose entries are not all zero for which AD = &quot; 0 0 0 0 # ? Explain your answer....
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