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Unformatted text preview: 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 . 4. (14 points) Do the columns of the following matrix span R 4 ? Justify your answer. 1 2 1 2 1 2 8 7 16 4 1 5 4 11 42152 5. (14 points) Find the inverse of A = " 4 3 3 2 # and use it to solve AX = " 22 3 1 0 5 # 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 = " 5 3 # into 2 31 and v = " 8 5 # into 7 2 1 (a) Find T (3 u + 5 v ) (b) Show that Span { u , v } = R 2 . (c) Use parametric vector form to describe the range of T ....
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This note was uploaded on 12/14/2009 for the course M 91795 taught by Professor Koch during the Spring '09 term at University of Texas at Austin.
 Spring '09
 KOCH

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