Exam1B900 - the columns of A . 4. (14 points) Are the...

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M340L EXAM 1B 9:00 FALL, 2009 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. (16 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. DO NOT USE A CALCULATOR!! SHOW ALL YOUR WORK STEP BY STEP!!! 1 2 4 0 0 2 2 4 8 4 1 17 1 2 4 3 0 11 0 0 0 - 2 1 - 5
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YOUR SCORE: /100 2. (14 points) Describe in detail the method used to determine whether p vectors in R q span R q and explain why the method works. 3. (14 points) Suppose A and C are p × p matrices such that CA = I p . Explain why the equation A x = 0 has only the trivial solution and then explain what this says about
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Unformatted text preview: the columns of A . 4. (14 points) Are the columns of the following matrix linearly independent? Justify your answer. 1 2 1 2 24 14 1 17 10-10-6 5. (14 points) Find the inverse of A = " 3 8 4 11 # and use it to solve AX = " 1 3 4 2-1 0 # 6. (14 points) Find the general ow pattern of the network shown in the gure. Assuming that the ows are all nonnegative, what is the largest possible value for x 3 ? 7. (14 points) Suppose the linear transformation T from R 2 to R 3 maps u = " 2 3 # into 3 2 1 and v = " 3 5 # into -6 1 8 (a) Find T (2 u + 3 v ) (b) Show that Span { u , v } = R 2 . (c) Use parametric vector form to describe the range of T ....
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Exam1B900 - the columns of A . 4. (14 points) Are the...

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